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Solving integrals/ 1/tan(h*x)

Integral of 1/tan(h*x) dx

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Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |     1       
 |  -------- dx
 |  tan(h*x)   
 |             
/              
0
∫011tan⁡(hx) dx\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       
 |                                                           
/
∫1tan⁡(hx) dx=C+log⁡(2sec⁡2(hx)−2)2h−log⁡(2sec⁡2(hx))2h\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}
Simplify
The answer [src] 
/       /1\   log(sin(h))                                  
|oo*sign|-| + -----------  for And(h > -oo, h < oo, h != 0)
<       \h/        h                                       
|                                                          
\           0                         otherwise
{∞sign⁡(1h)+log⁡(sin⁡(h))hfor h>−∞∧h<∞∧h≠00otherwise\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
{∞sign⁡(1h)+log⁡(sin⁡(h))hfor h>−∞∧h<∞∧h≠00otherwise\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.

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