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x^2sin(3x)^3

Integral of x^2sin(3x)^3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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 |   2    3        
 |  x *sin (3*x) dx
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$$\int\limits_{0}^{1} x^{2} \sin^{3}{\left(3 x \right)}\, dx$$
Integral(x^2*sin(3*x)^3, (x, 0, 1))
The answer (Indefinite) [src]
  /                                                                                                                                             
 |                             3           2    3                3              2                  2    2                        2              
 |  2    3               40*cos (3*x)   2*x *cos (3*x)   14*x*sin (3*x)   14*sin (3*x)*cos(3*x)   x *sin (3*x)*cos(3*x)   4*x*cos (3*x)*sin(3*x)
 | x *sin (3*x) dx = C + ------------ - -------------- + -------------- + --------------------- - --------------------- + ----------------------
 |                           729              9                81                  243                      3                       27          
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$$\int x^{2} \sin^{3}{\left(3 x \right)}\, dx = C - \frac{x^{2} \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{3} - \frac{2 x^{2} \cos^{3}{\left(3 x \right)}}{9} + \frac{14 x \sin^{3}{\left(3 x \right)}}{81} + \frac{4 x \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{27} + \frac{14 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{243} + \frac{40 \cos^{3}{\left(3 x \right)}}{729}$$
The graph
The answer [src]
               3            3            2                  2          
   40   122*cos (3)   14*sin (3)   67*sin (3)*cos(3)   4*cos (3)*sin(3)
- --- - ----------- + ---------- - ----------------- + ----------------
  729       729           81              243                 27       
$$- \frac{40}{729} + \frac{14 \sin^{3}{\left(3 \right)}}{81} - \frac{67 \sin^{2}{\left(3 \right)} \cos{\left(3 \right)}}{243} + \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(3 \right)}}{27} - \frac{122 \cos^{3}{\left(3 \right)}}{729}$$
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               3            3            2                  2          
   40   122*cos (3)   14*sin (3)   67*sin (3)*cos(3)   4*cos (3)*sin(3)
- --- - ----------- + ---------- - ----------------- + ----------------
  729       729           81              243                 27       
$$- \frac{40}{729} + \frac{14 \sin^{3}{\left(3 \right)}}{81} - \frac{67 \sin^{2}{\left(3 \right)} \cos{\left(3 \right)}}{243} + \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(3 \right)}}{27} - \frac{122 \cos^{3}{\left(3 \right)}}{729}$$
-40/729 - 122*cos(3)^3/729 + 14*sin(3)^3/81 - 67*sin(3)^2*cos(3)/243 + 4*cos(3)^2*sin(3)/27
Numerical answer [src]
0.133920660516566
0.133920660516566
The graph
Integral of x^2sin(3x)^3 dx

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