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Solving integrals/ xcos²(3x)

Integral of xcos²(3x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi               
 --               
 2                
  /               
 |                
 |       2        
 |  x*cos (3*x) dx
 |                
/                 
0
$$\int\limits_{0}^{\frac{\pi}{2}} x \cos^{2}{\left(3 x \right)}\, dx$$ 
Integral(x*cos(3*x)^2, (x, 0, pi/2))
The answer (Indefinite) [src] 
  /                                                                                  
 |                         2         2    2         2    2                           
 |      2               sin (3*x)   x *cos (3*x)   x *sin (3*x)   x*cos(3*x)*sin(3*x)
 | x*cos (3*x) dx = C - --------- + ------------ + ------------ + -------------------
 |                          36           4              4                  6         
/
$$\int x \cos^{2}{\left(3 x \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(3 x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(3 x \right)}}{4} + \frac{x \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{6} - \frac{\sin^{2}{\left(3 x \right)}}{36}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         2
  1    pi 
- -- + ---
  36    16
$$- \frac{1}{36} + \frac{\pi^{2}}{16}$$ 
=
= 
         2
  1    pi 
- -- + ---
  36    16
$$- \frac{1}{36} + \frac{\pi^{2}}{16}$$ 
-1/36 + pi^2/16
Numerical answer [src] 
0.589072497290307
0.589072497290307

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

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