What is the integral of sin(x)cos^8(x) ?

The integral of sin(x)cos^8(x) is -(cos^9(x))/9+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)cos^8(x)

\int sin (x) cos^{8} (x) d x

- \frac{cos ^{9} ( x )}{9} + C

Solution steps

\int sin (x) cos^{8} (x) d x

Apply u-substitution

: \int - u^{8} d u

= \int - u^{8} d u

Take the constant out:

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

= - \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= - \frac{u ^{9}}{9}

Substitute back

u = cos (x)

= - \frac{cos ^{9} ( x )}{9}

Add a constant to the solution

= - \frac{cos ^{9} ( x )}{9} + C

\int 3 x^{2} x d x

\int (x - 7) d x

\int sin (\frac{π}{x}) d x

\int \frac{2 x ^{4} + 3 x ^{2} + 4}{x ^{2} + 1} d x

What is the integral of sin(x)cos^8(x) ?
The integral of sin(x)cos^8(x) is -(cos^9(x))/9+C