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

The integral of-sin(x)*cos^2(x) is 1/3 cos^3(x)+C

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

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

\frac{1}{3} cos^{3} (x) + C

Solution steps

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

Take the constant out:

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

= - \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})

Simplify

- (- \frac{cos ^{3} ( x )}{3}) : \frac{1}{3} cos^{3} (x)

= \frac{1}{3} cos^{3} (x)

Add a constant to the solution

= \frac{1}{3} cos^{3} (x) + C

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(1.01)^{x} + 0.3 3^{x}

4 \cdot (\frac{3}{2})^{x}

\frac{d}{d r} (\frac{2 k}{r} + 2 π r^{2})

What is the integral of-sin(x)*cos^2(x) ?
The integral of-sin(x)*cos^2(x) is 1/3 cos^3(x)+C