What is the integral of cos^{(5)}(5x)sin(5x) ?

The integral of cos^{(5)}(5x)sin(5x) is -1/30 cos^6(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^{(5)}(5x)sin(5x)

\int cos^{(5)} (5 x) sin (5 x) d x

- \frac{1}{30} cos^{6} (5 x) + C

Solution steps

\int cos^{5} (5 x) sin (5 x) d x

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{5}{6} u^{\frac{6}{5}}

= - \frac{1}{25} \cdot \frac{5}{6} u^{\frac{6}{5}}

Substitute back

u = cos^{5} (5 x)

= - \frac{1}{25} \cdot \frac{5}{6} (cos^{5} (5 x))^{\frac{6}{5}}

Simplify

- \frac{1}{25} \cdot \frac{5}{6} (cos^{5} (5 x))^{\frac{6}{5}} : - \frac{1}{30} cos^{6} (5 x)

= - \frac{1}{30} cos^{6} (5 x)

Add a constant to the solution

= - \frac{1}{30} cos^{6} (5 x) + C

\int_{0}^{9} 3 x - x d x

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

\int x e^{3} d x

- \frac{48 x}{( x ^{2} + 12 ) ^{2}}

\int_{0}^{9} \frac{1}{x ^{2} - 6 x + 5} d x

What is the integral of cos^{(5)}(5x)sin(5x) ?
The integral of cos^{(5)}(5x)sin(5x) is -1/30 cos^6(5x)+C