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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u^{2} d u

= - \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x + 3}{x})

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\frac{d}{d x} (5^{(6 x^{2} - 7 x) (8 x^{2} + 9)})

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