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

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

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

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

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

Solution steps

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

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

\int 2 d t = 2 t

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

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

Add a constant to the solution

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

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