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Solving integrals/ sin^4x*d*sin(x)

Integral of sin^4x*d*sin(x) 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)*d*sin(x) dx
 |                     
/                      
0
$$\int\limits_{0}^{1} d \sin^{4}{\left(x \right)} \sin{\left(x \right)}\, dx$$ 
Integral((sin(x)^4*d)*sin(x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                              
 |                             /       5                            3       2   \
 |    4                        |  8*cos (x)      4             4*cos (x)*sin (x)|
 | sin (x)*d*sin(x) dx = C + d*|- --------- - sin (x)*cos(x) - -----------------|
 |                             \      15                               3        /
/
$$\int d \sin^{4}{\left(x \right)} \sin{\left(x \right)}\, dx = C + d \left(- \sin^{4}{\left(x \right)} \cos{\left(x \right)} - \frac{4 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \frac{8 \cos^{5}{\left(x \right)}}{15}\right)$$
Simplify
The answer [src] 
        /             5           3   \
8*d     |          cos (1)   2*cos (1)|
--- + d*|-cos(1) - ------- + ---------|
 15     \             5          3    /
$$d \left(- \cos{\left(1 \right)} - \frac{\cos^{5}{\left(1 \right)}}{5} + \frac{2 \cos^{3}{\left(1 \right)}}{3}\right) + \frac{8 d}{15}$$ 
=
= 
        /             5           3   \
8*d     |          cos (1)   2*cos (1)|
--- + d*|-cos(1) - ------- + ---------|
 15     \             5          3    /
$$d \left(- \cos{\left(1 \right)} - \frac{\cos^{5}{\left(1 \right)}}{5} + \frac{2 \cos^{3}{\left(1 \right)}}{3}\right) + \frac{8 d}{15}$$ 
8*d/15 + d*(-cos(1) - cos(1)^5/5 + 2*cos(1)^3/3)

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

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