Integral of 1/tan(h*x) dx
The solution
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
|
/
$$\int \frac{1}{\tan{\left(h x \right)}}\, dx = C + \frac{\log{\left(2 \sec^{2}{\left(h x \right)} - 2 \right)}}{2 h} - \frac{\log{\left(2 \sec^{2}{\left(h x \right)} \right)}}{2 h}$$
/ /1\ log(sin(h))
|oo*sign|-| + ----------- for And(h > -oo, h < oo, h != 0)
< \h/ h
|
\ 0 otherwise
$$\begin{cases} \infty \operatorname{sign}{\left(\frac{1}{h} \right)} + \frac{\log{\left(\sin{\left(h \right)} \right)}}{h} & \text{for}\: h > -\infty \wedge h < \infty \wedge h \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
/ /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.