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  • Identical expressions

  • (cos^ three)*x*sinx
  • ( co sinus of e of cubed ) multiply by x multiply by sinus of x
  • ( co sinus of e of to the power of three) multiply by x multiply by sinus of x
  • (cos3)*x*sinx
  • cos3*x*sinx
  • (cos³)*x*sinx
  • (cos to the power of 3)*x*sinx
  • (cos^3)xsinx
  • (cos3)xsinx
  • cos3xsinx
  • cos^3xsinx
  • (cos^3)*x*sinxdx
Solving integrals/ (cos^3)*x*sinx

Integral of (cos^3)*x*sinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                    
 --                    
 2                     
  /                    
 |                     
 |     3               
 |  cos (x)*x*sin(x) dx
 |                     
/                      
0
$$\int\limits_{0}^{\frac{\pi}{2}} x \cos^{3}{\left(x \right)} \sin{\left(x \right)}\, dx$$ 
Integral((cos(x)^3*x)*sin(x), (x, 0, pi/2))
The answer (Indefinite) [src] 
  /                                                                                                               
 |                                  4             4           3                  3                    2       2   
 |    3                      5*x*cos (x)   3*x*sin (x)   3*sin (x)*cos(x)   5*cos (x)*sin(x)   3*x*cos (x)*sin (x)
 | cos (x)*x*sin(x) dx = C - ----------- + ----------- + ---------------- + ---------------- + -------------------
 |                                32            32              32                 32                   16        
/
$$\int x \cos^{3}{\left(x \right)} \sin{\left(x \right)}\, dx = C + \frac{3 x \sin^{4}{\left(x \right)}}{32} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} - \frac{5 x \cos^{4}{\left(x \right)}}{32} + \frac{3 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{32} + \frac{5 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{32}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
3*pi
----
 64
$$\frac{3 \pi}{64}$$ 
=
= 
3*pi
----
 64
$$\frac{3 \pi}{64}$$ 
3*pi/64
Numerical answer [src] 
0.147262155637022
0.147262155637022

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

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