What is the integral of 2+cos^2(x)sin(x) ?

The integral of 2+cos^2(x)sin(x) is 2x-(cos^3(x))/3+C

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integral of 2+cos^2(x)sin(x)

\int 2 + cos^{2} (x) sin (x) d x

2 x - \frac{cos ^{3} ( x )}{3} + C

Solution steps

\int 2 + cos^{2} (x) sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d x + \int cos^{2} (x) sin (x) d x

\int 2 d x = 2 x

\int cos^{2} (x) sin (x) d x = - \frac{cos ^{3} ( x )}{3}

= 2 x - \frac{cos ^{3} ( x )}{3}

Add a constant to the solution

= 2 x - \frac{cos ^{3} ( x )}{3} + C

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What is the integral of 2+cos^2(x)sin(x) ?
The integral of 2+cos^2(x)sin(x) is 2x-(cos^3(x))/3+C