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sin^22x×cosx
Solving integrals/ sin^22x×cosx

Integral of sin^22x×cosx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  sin  (x)*cos(x) dx
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∫01sin⁡22(x)cos⁡(x) dx\int\limits_{0}^{1} \sin^{22}{\left(x \right)} \cos{\left(x \right)}\, dx 
Integral(sin(x)^22*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:

    ∫u22 du\int u^{22}\, du

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

      ∫u22 du=u2323\int u^{22}\, du = \frac{u^{23}}{23}

    Now substitute uu back in:

    sin⁡23(x)23\frac{\sin^{23}{\left(x \right)}}{23}

  2. Add the constant of integration:

    sin⁡23(x)23+constant\frac{\sin^{23}{\left(x \right)}}{23}+ \mathrm{constant}

The answer is:

sin⁡23(x)23+constant\frac{\sin^{23}{\left(x \right)}}{23}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
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 |    22                    sin  (x)
 | sin  (x)*cos(x) dx = C + --------
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∫sin⁡22(x)cos⁡(x) dx=sin⁡23(x)23+C\int \sin^{22}{\left(x \right)} \cos{\left(x \right)}\, dx = \frac{\sin^{23}{\left(x \right)}}{23} + C
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.000.02
Plot the graph f(x)
The answer [src] 
   23   
sin  (1)
--------
   23
sin⁡23123{{\sin ^{23}1}\over{23}} 
=
= 
   23   
sin  (1)
--------
   23
sin⁡23(1)23\frac{\sin^{23}{\left(1 \right)}}{23}
Simplify
Numerical answer [src] 
0.000820677466522084
0.000820677466522084
The graph
Integral of sin^22x×cosx dx

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

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