What is the integral of 2sin^6(x)cos(x) ?

The integral of 2sin^6(x)cos(x) is 2/7 sin^7(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2sin^6(x)cos(x)

\int 2 sin^{6} (x) cos (x) d x

\frac{2}{7} sin^{7} (x) + C

Solution steps

\int 2 sin^{6} (x) cos (x) d x

Take the constant out:

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

= 2 \cdot \int sin^{6} (x) cos (x) d x

Apply u-substitution

: \int u^{6} d u

= 2 \cdot \int u^{6} d u

Apply the Power Rule

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

= 2 \cdot \frac{u ^{7}}{7}

Substitute back

u = sin (x)

= 2 \cdot \frac{sin ^{7} ( x )}{7}

Simplify

2 \cdot \frac{sin ^{7} ( x )}{7} : \frac{2}{7} sin^{7} (x)

= \frac{2}{7} sin^{7} (x)

Add a constant to the solution

= \frac{2}{7} sin^{7} (x) + C

\int \frac{( x ^{3} )}{x ^{2} + 9} d x

x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}}

\int 5 x^{24} d x

\int 6 x^{\frac{2}{5}} d x

tan (5 x)

What is the integral of 2sin^6(x)cos(x) ?
The integral of 2sin^6(x)cos(x) is 2/7 sin^7(x)+C