What is the integral of cos^3(5x)sin(5x) ?

The integral of cos^3(5x)sin(5x) is -1/20 cos^4(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cos^3(5x)sin(5x)

\int cos^{3} (5 x) sin (5 x) d x

- \frac{1}{20} cos^{4} (5 x) + C

Solution steps

\int cos^{3} (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{1}{15} \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = cos^{3} (5 x)

= - \frac{1}{15} \cdot \frac{3}{4} (cos^{3} (5 x))^{\frac{4}{3}}

Simplify

- \frac{1}{15} \cdot \frac{3}{4} (cos^{3} (5 x))^{\frac{4}{3}} : - \frac{1}{20} cos^{4} (5 x)

= - \frac{1}{20} cos^{4} (5 x)

Add a constant to the solution

= - \frac{1}{20} cos^{4} (5 x) + C

What is the integral of cos^3(5x)sin(5x) ?
The integral of cos^3(5x)sin(5x) is -1/20 cos^4(5x)+C