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Identical expressions
- cos^22x-sin^22x
- co sinus of e of squared 2x minus sinus of squared 2x
- cos22x-sin22x
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Similar expressions
- cos^22x+sin^22x
Integral of cos^22x-sin^22x dx
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[src]
pi -- 8 / | | / 22 22 \ | \cos (x) - sin (x)/ dx | / 0
$$\int\limits_{0}^{\frac{\pi}{8}} \left(- \sin^{22}{\left(x \right)} + \cos^{22}{\left(x \right)}\right)\, dx$$
Integral(cos(x)^22 - sin(x)^22, (x, 0, pi/8))
The graph
The answer
[src]
___________ 21/2 21/2 ___________ ___________ 19/2 19/2 ___________ ___________ 17/2 17/2 ___________ ___________ 13/2 13/2 ___________ ___________ 15/2 15/2 ___________ ___________ 9/2 9/2 ___________ ___________ 11/2 11/2 ___________ ___________ 7/2 7/2 ___________ ___________ 3/2 3/2 ___________ ___________ 5/2 5/2 ___________ ___________ ___________
/ ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___
/ 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 / 1 \/ 2
/ - - ----- *|- + -----| |- - -----| * / - + ----- 21* / - - ----- *|- + -----| 21*|- - -----| * / - + ----- 133* / - - ----- *|- + -----| 133*|- - -----| * / - + ----- 323* / - - ----- *|- + -----| 323*|- - -----| * / - + ----- 2261* / - - ----- *|- + -----| 2261*|- - -----| * / - + ----- 4199* / - - ----- *|- + -----| 4199*|- - -----| * / - + ----- 4199* / - - ----- *|- + -----| 4199*|- - -----| * / - + ----- 12597* / - - ----- *|- + -----| 12597*|- - -----| * / - + ----- 29393* / - - ----- *|- + -----| 29393*|- - -----| * / - + ----- 29393* / - - ----- *|- + -----| 29393*|- - -----| * / - + ----- 88179* / - - ----- * / - + -----
\/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \/ 2 4
-------------------------------- + -------------------------------- + ----------------------------------- + ----------------------------------- + ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------- + ------------------------------------- + ------------------------------------ + ------------------------------------ + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ---------------------------------------
22 22 440 440 2640 2640 5632 5632 42240 42240 61440 61440 67584 67584 163840 163840 262144 262144 327680 327680 262144
$$\frac{\left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{21}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{22} + \frac{21 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{19}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{440} + \frac{133 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{17}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2640} + \frac{2261 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{15}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{42240} + \frac{323 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{13}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{5632} + \frac{4199 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{11}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{67584} + \frac{4199 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{9}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{61440} + \frac{12597 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{7}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{163840} + \frac{29393 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{5}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{327680} + \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{21}{2}}}{22} + \frac{21 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{19}{2}}}{440} + \frac{133 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{17}{2}}}{2640} + \frac{29393 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{3}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{262144} + \frac{2261 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{15}{2}}}{42240} + \frac{323 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{13}{2}}}{5632} + \frac{4199 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{11}{2}}}{67584} + \frac{4199 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{9}{2}}}{61440} + \frac{12597 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{7}{2}}}{163840} + \frac{29393 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{5}{2}}}{327680} + \frac{29393 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{3}{2}}}{262144} + \frac{88179 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{262144}$$
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___________ 21/2 21/2 ___________ ___________ 19/2 19/2 ___________ ___________ 17/2 17/2 ___________ ___________ 13/2 13/2 ___________ ___________ 15/2 15/2 ___________ ___________ 9/2 9/2 ___________ ___________ 11/2 11/2 ___________ ___________ 7/2 7/2 ___________ ___________ 3/2 3/2 ___________ ___________ 5/2 5/2 ___________ ___________ ___________
/ ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___\ / ___\ / ___ / ___ / ___
/ 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 |1 \/ 2 | |1 \/ 2 | / 1 \/ 2 / 1 \/ 2 / 1 \/ 2
/ - - ----- *|- + -----| |- - -----| * / - + ----- 21* / - - ----- *|- + -----| 21*|- - -----| * / - + ----- 133* / - - ----- *|- + -----| 133*|- - -----| * / - + ----- 323* / - - ----- *|- + -----| 323*|- - -----| * / - + ----- 2261* / - - ----- *|- + -----| 2261*|- - -----| * / - + ----- 4199* / - - ----- *|- + -----| 4199*|- - -----| * / - + ----- 4199* / - - ----- *|- + -----| 4199*|- - -----| * / - + ----- 12597* / - - ----- *|- + -----| 12597*|- - -----| * / - + ----- 29393* / - - ----- *|- + -----| 29393*|- - -----| * / - + ----- 29393* / - - ----- *|- + -----| 29393*|- - -----| * / - + ----- 88179* / - - ----- * / - + -----
\/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \2 4 / \2 4 / \/ 2 4 \/ 2 4 \/ 2 4
-------------------------------- + -------------------------------- + ----------------------------------- + ----------------------------------- + ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------- + ------------------------------------- + ------------------------------------ + ------------------------------------ + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ------------------------------------- + ---------------------------------------
22 22 440 440 2640 2640 5632 5632 42240 42240 61440 61440 67584 67584 163840 163840 262144 262144 327680 327680 262144
$$\frac{\left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{21}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{22} + \frac{21 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{19}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{440} + \frac{133 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{17}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2640} + \frac{2261 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{15}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{42240} + \frac{323 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{13}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{5632} + \frac{4199 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{11}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{67584} + \frac{4199 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{9}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{61440} + \frac{12597 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{7}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{163840} + \frac{29393 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{5}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{327680} + \frac{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{21}{2}}}{22} + \frac{21 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{19}{2}}}{440} + \frac{133 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{17}{2}}}{2640} + \frac{29393 \left(\frac{1}{2} - \frac{\sqrt{2}}{4}\right)^{\frac{3}{2}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{262144} + \frac{2261 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{15}{2}}}{42240} + \frac{323 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{13}{2}}}{5632} + \frac{4199 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{11}{2}}}{67584} + \frac{4199 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{9}{2}}}{61440} + \frac{12597 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{7}{2}}}{163840} + \frac{29393 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{5}{2}}}{327680} + \frac{29393 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \left(\frac{\sqrt{2}}{4} + \frac{1}{2}\right)^{\frac{3}{2}}}{262144} + \frac{88179 \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{262144}$$
sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(21/2)/22 + (1/2 - sqrt(2)/4)^(21/2)*sqrt(1/2 + sqrt(2)/4)/22 + 21*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(19/2)/440 + 21*(1/2 - sqrt(2)/4)^(19/2)*sqrt(1/2 + sqrt(2)/4)/440 + 133*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(17/2)/2640 + 133*(1/2 - sqrt(2)/4)^(17/2)*sqrt(1/2 + sqrt(2)/4)/2640 + 323*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(13/2)/5632 + 323*(1/2 - sqrt(2)/4)^(13/2)*sqrt(1/2 + sqrt(2)/4)/5632 + 2261*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(15/2)/42240 + 2261*(1/2 - sqrt(2)/4)^(15/2)*sqrt(1/2 + sqrt(2)/4)/42240 + 4199*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(9/2)/61440 + 4199*(1/2 - sqrt(2)/4)^(9/2)*sqrt(1/2 + sqrt(2)/4)/61440 + 4199*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(11/2)/67584 + 4199*(1/2 - sqrt(2)/4)^(11/2)*sqrt(1/2 + sqrt(2)/4)/67584 + 12597*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(7/2)/163840 + 12597*(1/2 - sqrt(2)/4)^(7/2)*sqrt(1/2 + sqrt(2)/4)/163840 + 29393*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(3/2)/262144 + 29393*(1/2 - sqrt(2)/4)^(3/2)*sqrt(1/2 + sqrt(2)/4)/262144 + 29393*sqrt(1/2 - sqrt(2)/4)*(1/2 + sqrt(2)/4)^(5/2)/327680 + 29393*(1/2 - sqrt(2)/4)^(5/2)*sqrt(1/2 + sqrt(2)/4)/327680 + 88179*sqrt(1/2 - sqrt(2)/4)*sqrt(1/2 + sqrt(2)/4)/262144
The graph
Use the examples entering the upper and lower limits of integration.