What is the integral of (cos^3(x)sin(x)) ?

The integral of (cos^3(x)sin(x)) is -(cos^4(x))/4+C

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integral of (cos^3(x)sin(x))

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

- \frac{cos ^{4} ( x )}{4} + C

Solution steps

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

Apply u-substitution

: \int - u^{3} d u

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= - \frac{u ^{4}}{4}

Substitute back

u = cos (x)

= - \frac{cos ^{4} ( x )}{4}

Add a constant to the solution

= - \frac{cos ^{4} ( x )}{4} + C

\frac{d}{d x} ((x - 1)^{\frac{2}{3}})

(x^{2} + y^{2}) d x + (2 x y) d y = 0

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 5

\frac{\partial}{\partial y} (e^{x y z^{4}} y z^{4})

\frac{\partial}{\partial y} (x^{2} - 2 x y + 2 y^{2})

What is the integral of (cos^3(x)sin(x)) ?
The integral of (cos^3(x)sin(x)) is -(cos^4(x))/4+C