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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of 1/5x
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Integral of (sec(x))^3
- Integral of lnx/sqrtx
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Integral of x^2*e^(x^3)
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Identical expressions
- (sec(x))^ three
- (sec(x)) cubed
- (sec(x)) to the power of three
- (sec(x))3
- secx3
- (sec(x))³
- (sec(x)) to the power of 3
- secx^3
- (sec(x))^3dx
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Similar expressions
- sec(x)^3
- tanxsecxsecx/4secx+9(secx)^3
Integral of (sec(x))^3 dx
The solution
You have entered
[src]
1 / | | 3 | sec (x) dx | / 0
$$\int\limits_{0}^{1} \sec^{3}{\left(x \right)}\, dx$$
Integral(sec(x)^3, (x, 0, 1))
The answer (Indefinite)
[src]
/ | | 3 log(-1 + sin(x)) log(1 + sin(x)) sin(x) | sec (x) dx = C - ---------------- + --------------- - -------------- | 4 4 2 / -2 + 2*sin (x)
$$\int \sec^{3}{\left(x \right)}\, dx = C - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}$$
The graph
The answer
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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.