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Solving integrals/ ∫(sen^4)xcosxdx

Integral of ∫(sen^4)xcosxdx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |     4               
 |  sin (x)*x*cos(x) dx
 |                     
/                      
0
$$\int\limits_{0}^{1} x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$ 
Integral((sin(x)^4*x)*cos(x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                    
 |                                5           5         4                  3       2   
 |    4                      8*cos (x)   x*sin (x)   sin (x)*cos(x)   4*cos (x)*sin (x)
 | sin (x)*x*cos(x) dx = C + --------- + --------- + -------------- + -----------------
 |                               75          5             5                  15       
/
$$\int x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{x \sin^{5}{\left(x \right)}}{5} + \frac{\sin^{4}{\left(x \right)} \cos{\left(x \right)}}{5} + \frac{4 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{15} + \frac{8 \cos^{5}{\left(x \right)}}{75}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
          5           5         4                  3       2   
  8    sin (1)   8*cos (1)   sin (1)*cos(1)   4*cos (1)*sin (1)
- -- + ------- + --------- + -------------- + -----------------
  75      5          75            5                  15
$$- \frac{8}{75} + \frac{8 \cos^{5}{\left(1 \right)}}{75} + \frac{4 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{15} + \frac{\sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{5} + \frac{\sin^{5}{\left(1 \right)}}{5}$$ 
=
= 
          5           5         4                  3       2   
  8    sin (1)   8*cos (1)   sin (1)*cos(1)   4*cos (1)*sin (1)
- -- + ------- + --------- + -------------- + -----------------
  75      5          75            5                  15
$$- \frac{8}{75} + \frac{8 \cos^{5}{\left(1 \right)}}{75} + \frac{4 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{15} + \frac{\sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{5} + \frac{\sin^{5}{\left(1 \right)}}{5}$$ 
-8/75 + sin(1)^5/5 + 8*cos(1)^5/75 + sin(1)^4*cos(1)/5 + 4*cos(1)^3*sin(1)^2/15
Numerical answer [src] 
0.0665824398736409
0.0665824398736409

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

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