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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of x^5*dx
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Integral of xsin(x+2)
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Integral of 1/(2+cosx)^2
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Integral of (1+x^4)^(1/2)
- Graphing y =:
- 1/cos^3x
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Identical expressions
- one /cos^3x
- 1 divide by co sinus of e of cubed x
- one divide by co sinus of e of cubed x
- 1/cos3x
- 1/cos³x
- 1/cos to the power of 3x
- 1 divide by cos^3x
- 1/cos^3xdx
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Similar expressions
- 1/(cos^3(x))
Integral of 1/cos^3x dx
The solution
You have entered
[src]
1 / | | 1 | ------- dx | 3 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\cos^{3}{\left(x \right)}}\, dx$$
Integral(1/(cos(x)^3), (x, 0, 1))
The answer (Indefinite)
[src]
/ | | 1 log(-1 + sin(x)) log(1 + sin(x)) sin(x) | ------- dx = C - ---------------- + --------------- - -------------- | 3 4 4 2 | cos (x) -2 + 2*sin (x) | /
$$\int \frac{1}{\cos^{3}{\left(x \right)}}\, dx = C - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}$$
The graph
The answer
[src]
log(1 - sin(1)) log(1 + sin(1)) sin(1)
- --------------- + --------------- - --------------
4 4 2
-2 + 2*sin (1)
$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}}$$
=
=
log(1 - sin(1)) log(1 + sin(1)) sin(1)
- --------------- + --------------- - --------------
4 4 2
-2 + 2*sin (1)
$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}}$$
-log(1 - sin(1))/4 + log(1 + sin(1))/4 - sin(1)/(-2 + 2*sin(1)^2)
The graph
Use the examples entering the upper and lower limits of integration.