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sinx^4cosx
Solving integrals/ sinx^4cosx

Integral of sinx^4cosx dx

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The solution

You have entered [src] 
 pi                  
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 |     4             
 |  sin (x)*cos(x) dx
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pi                   
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2
∫π2πsin⁡4(x)cos⁡(x) dx\int\limits_{\frac{\pi}{2}}^{\pi} \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx 
Integral(sin(x)^4*cos(x), (x, pi/2, pi))
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 + -------
 |                            5   
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∫sin⁡4(x)cos⁡(x) dx=C+sin⁡5(x)5\int \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{5}{\left(x \right)}}{5}
Simplify
The graph
1.61.71.81.92.02.12.22.32.42.52.62.72.82.93.03.10.5-0.5
Plot the graph f(x)
The answer [src] 
-1/5
−15- \frac{1}{5} 
=
= 
-1/5
−15- \frac{1}{5}
Упростить
Numerical answer [src] 
-0.2
-0.2
The graph
Integral of sinx^4cosx dx

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

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