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

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

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

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

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

Solution steps

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

Simplify

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

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 (x)

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

Add a constant to the solution

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

4 x^{2} + x y + 4 y^{2} = 9, (1, 1)

\frac{d}{d x} (3 x cot (4 x - 2))

y = x^{2} - 1, y = 8

\frac{1}{x}, \frac{5}{x}, x, 3 x

\int_{- π}^{π} sin (3 x) d x

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