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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of sec^3(x)
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Integral of e^y
- Integral of |x|
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Integral of xe^(x^2)
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Identical expressions
- sec^ three (x)
- sec cubed (x)
- sec to the power of three (x)
- sec3(x)
- sec3x
- sec³(x)
- sec to the power of 3(x)
- sec^3x
- sec^3(x)dx
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Similar expressions
- tanxsec^3x
- sec^3xdx
Integral of sec^3(x) dx
The solution
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[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.