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How to use it?
- Integral of d{x}:
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Integral of cos(x)*exp(x)
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Integral of sin(x)^2*cos(x)^4
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Integral of 2e^(-2x)
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Integral of x^3*ln(x)
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Identical expressions
- sec(x)(sec²(x))
- secxsec²x
- sec(x)(sec²(x))dx
Integral of sec(x)(sec²(x)) dx
The solution
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[src]
1 / | | 2 | sec(x)*sec (x) dx | / 0
$$\int\limits_{0}^{1} \sec{\left(x \right)} \sec^{2}{\left(x \right)}\, dx$$
Integral(sec(x)*sec(x)^2, (x, 0, 1))
The answer (Indefinite)
[src]
/ | | 2 log(-1 + sin(x)) log(1 + sin(x)) sin(x) | sec(x)*sec (x) dx = C - ---------------- + --------------- - -------------- | 4 4 2 / -2 + 2*sin (x)
$$\int \sec{\left(x \right)} \sec^{2}{\left(x \right)}\, dx = C - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}$$
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)
Use the examples entering the upper and lower limits of integration.