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xtan^2x
Solving integrals/ xtan^2x

Integral of xtan^2x dx

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The solution

You have entered [src] 
 pi             
 --             
 3              
  /             
 |              
 |       2      
 |  x*tan (x) dx
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/               
0
∫0π3xtan⁡2(x) dx\int\limits_{0}^{\frac{\pi}{3}} x \tan^{2}{\left(x \right)}\, dx 
Integral(x*tan(x)^2, (x, 0, pi/3))
The answer (Indefinite) [src] 
  /                                                   
 |                     2      /       2   \           
 |      2             x    log\1 + tan (x)/           
 | x*tan (x) dx = C - -- - ---------------- + x*tan(x)
 |                    2           2                   
/
∫xtan⁡2(x) dx=C−x22+xtan⁡(x)−log⁡(tan⁡2(x)+1)2\int x \tan^{2}{\left(x \right)}\, dx = C - \frac{x^{2}}{2} + x \tan{\left(x \right)} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2}
Simplify
The graph
0.000.100.200.300.400.500.600.700.800.901.0005
Plot the graph f(x)
The answer [src] 
             2        ___
  log(4)   pi    pi*\/ 3 
- ------ - --- + --------
    2       18      3
−log⁡(4)2−π218+3π3- \frac{\log{\left(4 \right)}}{2} - \frac{\pi^{2}}{18} + \frac{\sqrt{3} \pi}{3} 
=
= 
             2        ___
  log(4)   pi    pi*\/ 3 
- ------ - --- + --------
    2       18      3
−log⁡(4)2−π218+3π3- \frac{\log{\left(4 \right)}}{2} - \frac{\pi^{2}}{18} + \frac{\sqrt{3} \pi}{3} 
-log(4)/2 - pi^2/18 + pi*sqrt(3)/3
Numerical answer [src] 
0.572340828058197
0.572340828058197
The graph
Integral of xtan^2x dx

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

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