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cos^10(x)*sin(x)*dx
Solving integrals/ cos^10(x)*sin(x)*dx

Integral of cos^10(x)*sin(x)*dx dx

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The solution

You have entered [src] 
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∫00cos⁡10(x)sin⁡(x)1 dx\int\limits_{0}^{0} \cos^{10}{\left(x \right)} \sin{\left(x \right)} 1\, dx
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Detail solution

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

    Then let du=−sin⁡(x)dxdu = - \sin{\left(x \right)} dx and substitute −du- du:

    ∫u10 du\int u^{10}\, du

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫(−u10) du=−∫u10 du\int \left(- u^{10}\right)\, du = - \int u^{10}\, du

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

        ∫u10 du=u1111\int u^{10}\, du = \frac{u^{11}}{11}

      So, the result is: −u1111- \frac{u^{11}}{11}

    Now substitute uu back in:

    −cos⁡11(x)11- \frac{\cos^{11}{\left(x \right)}}{11}

  2. Add the constant of integration:

    −cos⁡11(x)11+constant- \frac{\cos^{11}{\left(x \right)}}{11}+ \mathrm{constant}

The answer is:

−cos⁡11(x)11+constant- \frac{\cos^{11}{\left(x \right)}}{11}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | cos  (x)*sin(x)*1 dx = C - --------
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−cos⁡11x11-{{\cos ^{11}x}\over{11}}
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The graph
0.001.000.100.200.300.400.500.600.700.800.900.10-0.10
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The answer [src] 
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Numerical answer [src] 
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The graph
Integral of cos^10(x)*sin(x)*dx dx

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

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