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

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

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integral of cos^2(θ)sin(θ)

\int cos^{2} (θ) sin (θ) d θ

- \frac{cos ^{3} ( θ )}{3} + C

Solution steps

\int cos^{2} (θ) sin (θ) d θ

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 (θ)

= - \frac{cos ^{3} ( θ )}{3}

Add a constant to the solution

= - \frac{cos ^{3} ( θ )}{3} + C

\int x e^{(x^{2})} d x

\int_{- 1}^{1} \frac{2 x}{( x + 5 ) ^{2}} d x

x \to 0 - lim (0)

3 t^{5}

\int (\frac{( x + 1 ) ( x - 2 )}{x}) d x

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