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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of x^2*exp(x^3)
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Integral of 1/(2x-1)
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Integral of x(x^2+1)^3
- Integral of e^(1/x)
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Identical expressions
- one /tan(h*x)
- 1 divide by tangent of (h multiply by x)
- one divide by tangent of (h multiply by x)
- 1/tan(hx)
- 1/tanhx
- 1 divide by tan(h*x)
- 1/tan(h*x)dx
Integral of 1/tan(h*x) dx
The solution
You have entered
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1 / | | 1 | -------- dx | tan(h*x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\tan{\left(h x \right)}}\, dx$$
Integral(1/tan(h*x), (x, 0, 1))
The answer (Indefinite)
[src]
/ | / 2 \ / 2 \ | 1 log\-2 + 2*sec (h*x)/ log\2*sec (h*x)/ | -------- dx = C + --------------------- - ---------------- | tan(h*x) 2*h 2*h | /
$$\int \frac{1}{\tan{\left(h x \right)}}\, dx = C + \frac{\log{\left(2 \sec^{2}{\left(h x \right)} - 2 \right)}}{2 h} - \frac{\log{\left(2 \sec^{2}{\left(h x \right)} \right)}}{2 h}$$
The answer
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/ /1\ log(sin(h)) |oo*sign|-| + ----------- for And(h > -oo, h < oo, h != 0) < \h/ h | \ 0 otherwise
$$\begin{cases} \infty \operatorname{sign}{\left(\frac{1}{h} \right)} + \frac{\log{\left(\sin{\left(h \right)} \right)}}{h} & \text{for}\: h > -\infty \wedge h < \infty \wedge h \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/ /1\ log(sin(h)) |oo*sign|-| + ----------- for And(h > -oo, h < oo, h != 0) < \h/ h | \ 0 otherwise
$$\begin{cases} \infty \operatorname{sign}{\left(\frac{1}{h} \right)} + \frac{\log{\left(\sin{\left(h \right)} \right)}}{h} & \text{for}\: h > -\infty \wedge h < \infty \wedge h \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((oo*sign(1/h) + log(sin(h))/h, (h > -oo)∧(h < oo)∧(Ne(h, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.