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cos^22x-sin^22x
Solving integrals/ cos^22x-sin^22x

Integral of cos^22x-sin^22x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                         
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 8                          
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 |  /   22         22   \   
 |  \cos  (x) - sin  (x)/ dx
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/                           
0
∫0π8(−sin⁡22(x)+cos⁡22(x)) dx\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
0.000.050.100.150.200.250.300.3502
Plot the graph f(x)
The answer [src] 
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               22                                 22                                  440                                   440                                   2640                                   2640                                   5632                                   5632                                   42240                                   42240                                  61440                                  61440                                   67584                                   67584                                   163840                                  163840                                  262144                                  262144                                  327680                                  327680                                   262144
(12−24)21224+1222+21(12−24)19224+12440+133(12−24)17224+122640+2261(12−24)15224+1242240+323(12−24)13224+125632+4199(12−24)11224+1267584+4199(12−24)9224+1261440+12597(12−24)7224+12163840+29393(12−24)5224+12327680+12−24(24+12)21222+2112−24(24+12)192440+13312−24(24+12)1722640+29393(12−24)3224+12262144+226112−24(24+12)15242240+32312−24(24+12)1325632+419912−24(24+12)11267584+419912−24(24+12)9261440+1259712−24(24+12)72163840+2939312−24(24+12)52327680+2939312−24(24+12)32262144+8817912−2424+12262144\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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\/    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   
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               22                                 22                                  440                                   440                                   2640                                   2640                                   5632                                   5632                                   42240                                   42240                                  61440                                  61440                                   67584                                   67584                                   163840                                  163840                                  262144                                  262144                                  327680                                  327680                                   262144
(12−24)21224+1222+21(12−24)19224+12440+133(12−24)17224+122640+2261(12−24)15224+1242240+323(12−24)13224+125632+4199(12−24)11224+1267584+4199(12−24)9224+1261440+12597(12−24)7224+12163840+29393(12−24)5224+12327680+12−24(24+12)21222+2112−24(24+12)192440+13312−24(24+12)1722640+29393(12−24)3224+12262144+226112−24(24+12)15242240+32312−24(24+12)1325632+419912−24(24+12)11267584+419912−24(24+12)9261440+1259712−24(24+12)72163840+2939312−24(24+12)52327680+2939312−24(24+12)32262144+8817912−2424+12262144\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
Numerical answer [src] 
0.248597001338501
0.248597001338501
The graph
Integral of cos^22x-sin^22x dx

    Use the examples entering the upper and lower limits of integration.

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