What is the integral of-13cos^3(x)sin(x) ?

The integral of-13cos^3(x)sin(x) is 13/4 cos^4(x)+C

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integral of-13cos^3(x)sin(x)

\int - 13 cos^{3} (x) sin (x) d x

\frac{13}{4} cos^{4} (x) + C

Solution steps

\int - 13 cos^{3} (x) sin (x) d x

Take the constant out:

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

= - 13 \cdot \int cos^{3} (x) sin (x) d x

Apply u-substitution

: \int - u^{3} d u

= - 13 \cdot \int - u^{3} d u

Take the constant out:

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

= - 13 (- \int u^{3} d u)

Apply the Power Rule

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

= - 13 (- \frac{u ^{4}}{4})

Substitute back

u = cos (x)

= - 13 (- \frac{cos ^{4} ( x )}{4})

Simplify

- 13 (- \frac{cos ^{4} ( x )}{4}) : \frac{13}{4} cos^{4} (x)

= \frac{13}{4} cos^{4} (x)

Add a constant to the solution

= \frac{13}{4} cos^{4} (x) + C

\int_{0}^{1} \frac{5}{x ( x + 1 )} d x

(2 x y + 2 x^{3} y) d x - (1 + x^{2}) d y = 0

x \to \infty lim (a x^{4} + b x^{2} + c)

x \to 0 lim (\frac{3 x - 1}{2 x})

\int_{0}^{1} \frac{ln ( x )}{x} d x

What is the integral of-13cos^3(x)sin(x) ?
The integral of-13cos^3(x)sin(x) is 13/4 cos^4(x)+C