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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= - \frac{u ^{3}}{3}

Substitute back

u = cos (t)

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

Add a constant to the solution

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

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