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Identical expressions
- six /(five √4x+√ two)+ one /cos^25x
- 6 divide by (5√4x plus √2) plus 1 divide by co sinus of e of squared 5x
- six divide by (five √4x plus √ two) plus one divide by co sinus of e of squared 5x
- 6/(5√4x+√2)+1/cos25x
- 6/5√4x+√2+1/cos25x
- 6/(5√4x+√2)+1/cos²5x
- 6/(5√4x+√2)+1/cos to the power of 25x
- 6/5√4x+√2+1/cos^25x
- 6 divide by (5√4x+√2)+1 divide by cos^25x
- 6/(5√4x+√2)+1/cos^25xdx
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Similar expressions
- 6/(5√4x+√2)-1/cos^25x
- 6/(5√4x-√2)+1/cos^25x
Integral of 6/(5√4x+√2)+1/cos^25x dx
The solution
You have entered
[src]
1 / | | / 6 1 \ | |----------------- + 1*--------| dx | | _____ ___ 25 | | \5*\/ 4*x + \/ 2 cos (x)/ | / 0
$$\int\limits_{0}^{1} \left(1 \cdot \frac{1}{\cos^{25}{\left(x \right)}} + \frac{6}{5 \sqrt{4 x} + \sqrt{2}}\right)\, dx$$
The answer (Indefinite)
[src]
/ | ___ 13 9 17 5 21 23 3 19 7 15 11 ___ / ___ ___\ | / 6 1 \ 676039*log(-1 + sin(x)) 6*\/ x 676039*log(1 + sin(x)) - 221803567050*sin (x) - 197767334710*sin (x) - 67013911107*sin (x) - 46038446685*sin (x) - 3904125225*sin (x) - 1741541175*sin(x) + 334639305*sin (x) + 12013258455*sin (x) + 20814564771*sin (x) + 114444262845*sin (x) + 144986993866*sin (x) + 245588699190*sin (x) 3*\/ 2 *log\\/ 2 + 10*\/ x / | |----------------- + 1*--------| dx = C - ----------------------- + ------- + ---------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------- | | _____ ___ 25 | 8388608 5 8388608 10 14 6 18 2 22 24 4 20 8 16 12 25 | \5*\/ 4*x + \/ 2 cos (x)/ 2076180480 - 1644334940160*sin (x) - 1644334940160*sin (x) - 456759705600*sin (x) - 456759705600*sin (x) - 24914165760*sin (x) - 24914165760*sin (x) + 2076180480*sin (x) + 137027911680*sin (x) + 137027911680*sin (x) + 1027709337600*sin (x) + 1027709337600*sin (x) + 1918390763520*sin (x) | /
$${{676039\,\log \left(\sin x+1\right)}\over{8388608}}-{{676039\,
\log \left(\sin x-1\right)}\over{8388608}}-{{334639305\,\sin ^{23}x-
3904125225\,\sin ^{21}x+20814564771\,\sin ^{19}x-67013911107\,\sin
^{17}x+144986993866\,\sin ^{15}x-221803567050\,\sin ^{13}x+
245588699190\,\sin ^{11}x-197767334710\,\sin ^9x+114444262845\,\sin
^7x-46038446685\,\sin ^5x+12013258455\,\sin ^3x-1741541175\,\sin x
}\over{2076180480\,\sin ^{24}x-24914165760\,\sin ^{22}x+137027911680
\,\sin ^{20}x-456759705600\,\sin ^{18}x+1027709337600\,\sin ^{16}x-
1644334940160\,\sin ^{14}x+1918390763520\,\sin ^{12}x-1644334940160
\,\sin ^{10}x+1027709337600\,\sin ^8x-456759705600\,\sin ^6x+
137027911680\,\sin ^4x-24914165760\,\sin ^2x+2076180480}}+6\,\left(
{{10\,\sqrt{x}+\sqrt{2}}\over{50}}-{{\log \left(10\,\sqrt{x}+\sqrt{2
}\right)}\over{25\,\sqrt{2}}}\right)$$
The graph
The answer
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13 9 17 5 21 23 3 19 7 15 11 ___ / ___\ ___ / ___\
6 676039*log(1 - sin(1)) 676039*log(1 + sin(1)) - 221803567050*sin (1) - 197767334710*sin (1) - 67013911107*sin (1) - 46038446685*sin (1) - 3904125225*sin (1) - 1741541175*sin(1) + 334639305*sin (1) + 12013258455*sin (1) + 20814564771*sin (1) + 114444262845*sin (1) + 144986993866*sin (1) + 245588699190*sin (1) 3*\/ 2 *log\10 + \/ 2 / 3*\/ 2 *log\\/ 2 /
- - ---------------------- + ---------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------- + ------------------
5 8388608 8388608 10 14 6 18 2 22 24 4 20 8 16 12 25 25
2076180480 - 1644334940160*sin (1) - 1644334940160*sin (1) - 456759705600*sin (1) - 456759705600*sin (1) - 24914165760*sin (1) - 24914165760*sin (1) + 2076180480*sin (1) + 137027911680*sin (1) + 137027911680*sin (1) + 1027709337600*sin (1) + 1027709337600*sin (1) + 1918390763520*sin (1)
$$- \frac{3 \sqrt{2} \log{\left(\sqrt{2} + 10 \right)}}{25} + \frac{676039 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{8388608} + \frac{3 \sqrt{2} \log{\left(\sqrt{2} \right)}}{25} - \frac{676039 \log{\left(- \sin{\left(1 \right)} + 1 \right)}}{8388608} + \frac{6}{5} - \frac{- 197767334710 \sin^{9}{\left(1 \right)} - 221803567050 \sin^{13}{\left(1 \right)} - 46038446685 \sin^{5}{\left(1 \right)} - 67013911107 \sin^{17}{\left(1 \right)} - 1741541175 \sin{\left(1 \right)} - 3904125225 \sin^{21}{\left(1 \right)} + 334639305 \sin^{23}{\left(1 \right)} + 20814564771 \sin^{19}{\left(1 \right)} + 12013258455 \sin^{3}{\left(1 \right)} + 144986993866 \sin^{15}{\left(1 \right)} + 114444262845 \sin^{7}{\left(1 \right)} + 245588699190 \sin^{11}{\left(1 \right)}}{- 1644334940160 \sin^{10}{\left(1 \right)} - 456759705600 \sin^{6}{\left(1 \right)} - 1644334940160 \sin^{14}{\left(1 \right)} - 456759705600 \sin^{18}{\left(1 \right)} - 24914165760 \sin^{2}{\left(1 \right)} - 24914165760 \sin^{22}{\left(1 \right)} + 2076180480 \sin^{24}{\left(1 \right)} + 2076180480 + 137027911680 \sin^{20}{\left(1 \right)} + 1027709337600 \sin^{16}{\left(1 \right)} + 137027911680 \sin^{4}{\left(1 \right)} + 1918390763520 \sin^{12}{\left(1 \right)} + 1027709337600 \sin^{8}{\left(1 \right)}}$$
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13 9 17 5 21 23 3 19 7 15 11 ___ / ___\ ___ / ___\
6 676039*log(1 - sin(1)) 676039*log(1 + sin(1)) - 221803567050*sin (1) - 197767334710*sin (1) - 67013911107*sin (1) - 46038446685*sin (1) - 3904125225*sin (1) - 1741541175*sin(1) + 334639305*sin (1) + 12013258455*sin (1) + 20814564771*sin (1) + 114444262845*sin (1) + 144986993866*sin (1) + 245588699190*sin (1) 3*\/ 2 *log\10 + \/ 2 / 3*\/ 2 *log\\/ 2 /
- - ---------------------- + ---------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------- + ------------------
5 8388608 8388608 10 14 6 18 2 22 24 4 20 8 16 12 25 25
2076180480 - 1644334940160*sin (1) - 1644334940160*sin (1) - 456759705600*sin (1) - 456759705600*sin (1) - 24914165760*sin (1) - 24914165760*sin (1) + 2076180480*sin (1) + 137027911680*sin (1) + 137027911680*sin (1) + 1027709337600*sin (1) + 1027709337600*sin (1) + 1918390763520*sin (1)
$$- \frac{3 \sqrt{2} \log{\left(\sqrt{2} + 10 \right)}}{25} + \frac{676039 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{8388608} + \frac{3 \sqrt{2} \log{\left(\sqrt{2} \right)}}{25} - \frac{676039 \log{\left(- \sin{\left(1 \right)} + 1 \right)}}{8388608} + \frac{6}{5} - \frac{- 197767334710 \sin^{9}{\left(1 \right)} - 221803567050 \sin^{13}{\left(1 \right)} - 46038446685 \sin^{5}{\left(1 \right)} - 67013911107 \sin^{17}{\left(1 \right)} - 1741541175 \sin{\left(1 \right)} - 3904125225 \sin^{21}{\left(1 \right)} + 334639305 \sin^{23}{\left(1 \right)} + 20814564771 \sin^{19}{\left(1 \right)} + 12013258455 \sin^{3}{\left(1 \right)} + 144986993866 \sin^{15}{\left(1 \right)} + 114444262845 \sin^{7}{\left(1 \right)} + 245588699190 \sin^{11}{\left(1 \right)}}{- 1644334940160 \sin^{10}{\left(1 \right)} - 456759705600 \sin^{6}{\left(1 \right)} - 1644334940160 \sin^{14}{\left(1 \right)} - 456759705600 \sin^{18}{\left(1 \right)} - 24914165760 \sin^{2}{\left(1 \right)} - 24914165760 \sin^{22}{\left(1 \right)} + 2076180480 \sin^{24}{\left(1 \right)} + 2076180480 + 137027911680 \sin^{20}{\left(1 \right)} + 1027709337600 \sin^{16}{\left(1 \right)} + 137027911680 \sin^{4}{\left(1 \right)} + 1918390763520 \sin^{12}{\left(1 \right)} + 1027709337600 \sin^{8}{\left(1 \right)}}$$
The graph
Use the examples entering the upper and lower limits of integration.