Mister Exam

Other calculators

xctg^2x
Solving integrals/ xctg^2x

Integral of xctg^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |       2      
 |  x*cot (x) dx
 |              
/               
0
∫01xcot⁡2(x) dx\int\limits_{0}^{1} x \cot^{2}{\left(x \right)}\, dx 
Integral(x*cot(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                               
 |                     2      /       2   \                       
 |      2             x    log\1 + tan (x)/     x                 
 | x*cot (x) dx = C - -- - ---------------- - ------ + log(tan(x))
 |                    2           2           tan(x)              
/
(sin⁡2(2 x)+cos⁡2(2 x)−2 cos⁡(2 x)+1) log⁡(sin⁡2x+cos⁡2x+2 cos⁡x+1)+(sin⁡2(2 x)+cos⁡2(2 x)−2 cos⁡(2 x)+1) log⁡(sin⁡2x+cos⁡2x−2 cos⁡x+1)−x2 sin⁡2(2 x)−4 x sin⁡(2 x)−x2 cos⁡2(2 x)+2 x2 cos⁡(2 x)−x22 sin⁡2(2 x)+2 cos⁡2(2 x)−4 cos⁡(2 x)+2{{\left(\sin ^2\left(2\,x\right)+\cos ^2\left(2\,x\right)-2\,\cos \left(2\,x\right)+1\right)\,\log \left(\sin ^2x+\cos ^2x+2\,\cos x+1 \right)+\left(\sin ^2\left(2\,x\right)+\cos ^2\left(2\,x\right)-2\, \cos \left(2\,x\right)+1\right)\,\log \left(\sin ^2x+\cos ^2x-2\, \cos x+1\right)-x^2\,\sin ^2\left(2\,x\right)-4\,x\,\sin \left(2\,x \right)-x^2\,\cos ^2\left(2\,x\right)+2\,x^2\,\cos \left(2\,x\right) -x^2}\over{2\,\sin ^2\left(2\,x\right)+2\,\cos ^2\left(2\,x\right)-4 \,\cos \left(2\,x\right)+2}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-500010000
Plot the graph f(x)
The answer [src] 
oo
%a{\it \%a} 
=
= 
oo
∞\infty
Simplify
Numerical answer [src] 
43.7757497717895
43.7757497717895
The graph
Integral of xctg^2x dx

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator