What is the integral of 7sin^6(x)cos(x) ?

The integral of 7sin^6(x)cos(x) is 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 7sin^6(x)cos(x)

\int 7 sin^{6} (x) cos (x) d x

sin^{7} (x) + C

Solution steps

\int 7 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

= 7 \cdot \int sin^{6} (x) cos (x) d x

Apply u-substitution

: \int u^{6} d u

= 7 \cdot \int u^{6} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Simplify

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

= sin^{7} (x)

Add a constant to the solution

= sin^{7} (x) + C

\int \frac{1}{e ^{2 y} - 2 e ^{y}} d y

f (x) = 6^{x} lo g_{5} (x)

\int_{0}^{2 π} cos^{2} (x) d x

\frac{\partial}{\partial y} (e^{3 x + 2 y})

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