What is the integral of-17sin^4(x)cos(x) ?

The integral of-17sin^4(x)cos(x) is -17/5 sin^5(x)+C

Popular >

integral of-17sin^4(x)cos(x)

\int - 17 sin^{4} (x) cos (x) d x

- \frac{17}{5} sin^{5} (x) + C

Solution steps

\int - 17 sin^{4} (x) cos (x) d x

Take the constant out:

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

= - 17 \cdot \int sin^{4} (x) cos (x) d x

Apply u-substitution

: \int u^{4} d u

= - 17 \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= - 17 \cdot \frac{u ^{5}}{5}

Substitute back

u = sin (x)

= - 17 \cdot \frac{sin ^{5} ( x )}{5}

Simplify

- 17 \cdot \frac{sin ^{5} ( x )}{5} : - \frac{17}{5} sin^{5} (x)

= - \frac{17}{5} sin^{5} (x)

Add a constant to the solution

= - \frac{17}{5} sin^{5} (x) + C

x^{3} \frac{d y}{d x} = x^{2} y - y^{3}

5 x^{\frac{1}{3}} - 5 x^{- \frac{2}{3}}

\frac{d}{d x} (lo g_{2} (7 - 3 x))

x \to 0 + lim ((tan (8 x))^{x})

(x^{2} + 1)^{x}

What is the integral of-17sin^4(x)cos(x) ?
The integral of-17sin^4(x)cos(x) is -17/5 sin^5(x)+C