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sin^4xcos
Solving integrals/ sin^4xcos

Integral of sin^4xcos dx

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The solution

You have entered [src] 
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 |  sin (x)*cos(x) dx
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∫01sin⁡4(x)cos⁡(x) dx\int\limits_{0}^{1} \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx 
Integral(sin(x)^4*cos(x), (x, 0, 1))
Detail solution

  1. Let u=sin⁡(x)u = \sin{\left(x \right)}.

    Then let du=cos⁡(x)dxdu = \cos{\left(x \right)} dx and substitute dudu:

    ∫u4 du\int u^{4}\, du

    1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫u4 du=u55\int u^{4}\, du = \frac{u^{5}}{5}

    Now substitute uu back in:

    sin⁡5(x)5\frac{\sin^{5}{\left(x \right)}}{5}

  2. Add the constant of integration:

    sin⁡5(x)5+constant\frac{\sin^{5}{\left(x \right)}}{5}+ \mathrm{constant}

The answer is:

sin⁡5(x)5+constant\frac{\sin^{5}{\left(x \right)}}{5}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                            5   
 |    4                    sin (x)
 | sin (x)*cos(x) dx = C + -------
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sin⁡5x5{{\sin ^5x}\over{5}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.000.50
Plot the graph f(x)
The answer [src] 
   5   
sin (1)
-------
   5
sin⁡515{{\sin ^51}\over{5}} 
=
= 
   5   
sin (1)
-------
   5
sin⁡5(1)5\frac{\sin^{5}{\left(1 \right)}}{5}
Simplify
Numerical answer [src] 
0.0843773191639561
0.0843773191639561
The graph
Integral of sin^4xcos dx

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

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