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sin^5(x)*sin^4(x)
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] 
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 |     5       4      
 |  sin (x)*sin (x) dx
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∫01sin⁡4(x)sin⁡5(x) dx\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    
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−cos⁡9x9+4 cos⁡7x7−6 cos⁡5x5+4 cos⁡3x3−cos⁡x-{{\cos ^9x}\over{9}}+{{4\,\cos ^7x}\over{7}}-{{6\,\cos ^5x}\over{5 }}+{{4\,\cos ^3x}\over{3}}-\cos x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.5-0.5
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
128315−35 cos⁡91−180 cos⁡71+378 cos⁡51−420 cos⁡31+315 cos⁡1315{{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⁡(1)−6cos⁡5(1)5−cos⁡9(1)9+4cos⁡7(1)7+4cos⁡3(1)3+128315- \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}
Упростить
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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