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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sin(5x+7)
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Integral of sin^8x/cos^8x
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Integral of 6x²dx
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Integral of sin(8x)cos(6x)
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Identical expressions
- sin^8x/cos^8x
- sinus of to the power of 8x divide by co sinus of e of to the power of 8x
- sin8x/cos8x
- sin⁸x/cos⁸x
- sin^8x divide by cos^8x
- sin^8x/cos^8xdx
Integral of sin^8x/cos^8x dx
The solution
You have entered
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1 / | | 8 | sin (x) | ------- dx | 8 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{\sin^{8}{\left(x \right)}}{\cos^{8}{\left(x \right)}}\, dx$$
Integral(sin(x)^8/(cos(x)^8), (x, 0, 1))
The answer (Indefinite)
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/ | | 8 5 3 7 | sin (x) sin(x) sin (x) sin (x) sin (x) | ------- dx = C + x - ------ - --------- + --------- + --------- | 8 cos(x) 5 3 7 | cos (x) 5*cos (x) 3*cos (x) 7*cos (x) | /
$${{15\,\tan ^7x-21\,\tan ^5x+35\,\tan ^3x-105\,\tan x}\over{105}}+x$$
The graph
The answer
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5 3 7
sin(1) sin (1) sin (1) sin (1)
1 - ------ - --------- + --------- + ---------
cos(1) 5 3 7
5*cos (1) 3*cos (1) 7*cos (1)
$${{15\,\tan ^71-21\,\tan ^51+35\,\tan ^31-105\,\tan 1}\over{105}}+1$$
=
=
5 3 7
sin(1) sin (1) sin (1) sin (1)
1 - ------ - --------- + --------- + ---------
cos(1) 5 3 7
5*cos (1) 3*cos (1) 7*cos (1)
$$- \frac{\sin^{5}{\left(1 \right)}}{5 \cos^{5}{\left(1 \right)}} - \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + 1 + \frac{\sin^{3}{\left(1 \right)}}{3 \cos^{3}{\left(1 \right)}} + \frac{\sin^{7}{\left(1 \right)}}{7 \cos^{7}{\left(1 \right)}}$$
The graph
Use the examples entering the upper and lower limits of integration.