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

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

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

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

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

Solution steps

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

\frac{d}{d x} (e^{4 x^{2 + 1}})

x \to 0 + lim (\frac{2}{x} - \frac{3}{2})

\int cos (x) (3 + 8 sin^{2} (x)) d x

x \to 3 + lim (\frac{3 x + 2}{x - 3})

\frac{d}{d x} (- e^{x} sin (x))

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