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sin^5(x)*sin^4(x)

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  • Identical expressions

  • sin^ five (x)*sin^ four (x)
  • sinus of to the power of 5(x) multiply by sinus of to the power of 4(x)
  • sinus of to the power of five (x) multiply by sinus of to the power of four (x)
  • sin5(x)*sin4(x)
  • sin5x*sin4x
  • sin⁵(x)*sin⁴(x)
  • sin^5(x)sin^4(x)
  • sin5(x)sin4(x)
  • sin5xsin4x
  • sin^5xsin^4x
  • sin^5(x)*sin^4(x)dx
Solving integrals/ sin^5(x)*sin^4(x)

Integral of sin^5(x)*sin^4(x) dx

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The solution

You have entered [src] 
  1                   
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 |                    
 |     5       4      
 |  sin (x)*sin (x) dx
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0
$$\int\limits_{0}^{1} \sin^{4}{\left(x \right)} \sin^{5}{\left(x \right)}\, dx$$ 
Integral(sin(x)^5*sin(x)^4, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                             
 |                                        5         9           3           7   
 |    5       4                      6*cos (x)   cos (x)   4*cos (x)   4*cos (x)
 | sin (x)*sin (x) dx = C - cos(x) - --------- - ------- + --------- + ---------
 |                                       5          9          3           7    
/
$$-{{\cos ^9x}\over{9}}+{{4\,\cos ^7x}\over{7}}-{{6\,\cos ^5x}\over{5 }}+{{4\,\cos ^3x}\over{3}}-\cos x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                    5         9           3           7   
128            6*cos (1)   cos (1)   4*cos (1)   4*cos (1)
--- - cos(1) - --------- - ------- + --------- + ---------
315                5          9          3           7
$${{128}\over{315}}-{{35\,\cos ^91-180\,\cos ^71+378\,\cos ^51-420\, \cos ^31+315\,\cos 1}\over{315}}$$ 
=
= 
                    5         9           3           7   
128            6*cos (1)   cos (1)   4*cos (1)   4*cos (1)
--- - cos(1) - --------- - ------- + --------- + ---------
315                5          9          3           7
$$- \cos{\left(1 \right)} - \frac{6 \cos^{5}{\left(1 \right)}}{5} - \frac{\cos^{9}{\left(1 \right)}}{9} + \frac{4 \cos^{7}{\left(1 \right)}}{7} + \frac{4 \cos^{3}{\left(1 \right)}}{3} + \frac{128}{315}$$
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Numerical answer [src] 
0.028342532187773
0.028342532187773
The graph
Integral of sin^5(x)*sin^4(x) dx

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

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