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Integral of (x^2sinxcos2x) dx

Limits of integration:

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The solution

You have entered [src]
  pi                      
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  4                       
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  |   2                   
  |  x *sin(x)*cos(2*x) dx
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-pi                       
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 4                        
$$\int\limits_{- \frac{\pi}{4}}^{\frac{\pi}{4}} x^{2} \sin{\left(x \right)} \cos{\left(2 x \right)}\, dx$$
Integral((x^2*sin(x))*cos(2*x), (x, -pi/4, pi/4))
The answer (Indefinite) [src]
  /                                                                                                                                                
 |                                              3         /       3            \                       3           2                    2          
 |  2                                     28*cos (x)    2 |  2*cos (x)         |                8*x*sin (x)   8*sin (x)*cos(x)   4*x*cos (x)*sin(x)
 | x *sin(x)*cos(2*x) dx = C - 2*cos(x) + ---------- + x *|- --------- + cos(x)| - 2*x*sin(x) + ----------- + ---------------- + ------------------
 |                                            27          \      3             /                     9               9                   3         
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$$\int x^{2} \sin{\left(x \right)} \cos{\left(2 x \right)}\, dx = C + x^{2} \left(- \frac{2 \cos^{3}{\left(x \right)}}{3} + \cos{\left(x \right)}\right) + \frac{8 x \sin^{3}{\left(x \right)}}{9} + \frac{4 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - 2 x \sin{\left(x \right)} + \frac{8 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{9} + \frac{28 \cos^{3}{\left(x \right)}}{27} - 2 \cos{\left(x \right)}$$
Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.