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

\int \frac{36 + ( ln ( 2 x ) ) ^{2}}{x} d x

\frac{d}{d x} (3 y) = 5

4 x e^{x}

\int sin (t^{3}) d t

f (x) = \frac{1 + x - 4 x}{x}

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