What is the integral of cos^6(x)sin(x) ?

The integral of cos^6(x)sin(x) is -(cos^7(x))/7+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^6(x)sin(x)

\int cos^{6} (x) sin (x) d x

- \frac{cos ^{7} ( x )}{7} + C

Solution steps

\int cos^{6} (x) sin (x) d x

Apply u-substitution

: \int - u^{6} d u

= \int - u^{6} d u

Take the constant out:

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

= - \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= - \frac{u ^{7}}{7}

Substitute back

u = cos (x)

= - \frac{cos ^{7} ( x )}{7}

Add a constant to the solution

= - \frac{cos ^{7} ( x )}{7} + C

y = 11 + cot^{2} (x)

\frac{d}{d x} (I n (x))

\int sin^{4} (θ) cos^{5} (θ) d θ

- x, \frac{1}{2} x - \frac{3}{2}, - 1, 3

\frac{d}{d t} (1 + t^{2})

What is the integral of cos^6(x)sin(x) ?
The integral of cos^6(x)sin(x) is -(cos^7(x))/7+C