What is the integral of sin^7(2x)cos(2x) ?

The integral of sin^7(2x)cos(2x) is 1/16 sin^8(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin^7(2x)cos(2x)

\int sin^{7} (2 x) cos (2 x) d x

\frac{1}{16} sin^{8} (2 x) + C

Solution steps

\int sin^{7} (2 x) cos (2 x) d x

Apply u-substitution

: \int \frac{7 u}{14} d u

= \int \frac{7 u}{14} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int 7 u d u

Apply the Power Rule

: \frac{7}{8} u^{\frac{8}{7}}

= \frac{1}{14} \cdot \frac{7}{8} u^{\frac{8}{7}}

Substitute back

u = sin^{7} (2 x)

= \frac{1}{14} \cdot \frac{7}{8} (sin^{7} (2 x))^{\frac{8}{7}}

Simplify

\frac{1}{14} \cdot \frac{7}{8} (sin^{7} (2 x))^{\frac{8}{7}} : \frac{1}{16} sin^{8} (2 x)

= \frac{1}{16} sin^{8} (2 x)

Add a constant to the solution

= \frac{1}{16} sin^{8} (2 x) + C

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

\frac{d y}{d x} = 3 y + a

f (x) = 13440 (2 x + 5)^{3}

\int \frac{3 x - 1}{x x ^{2} - 25} d x

\frac{d}{d x} (ln (3 x - 2))

What is the integral of sin^7(2x)cos(2x) ?
The integral of sin^7(2x)cos(2x) is 1/16 sin^8(2x)+C