What is the integral of 5xsin(5x) ?

The integral of 5xsin(5x) is -xcos(5x)+1/5 sin(5x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5xsin(5x)

\int 5 x sin (5 x) d x

- x cos (5 x) + \frac{1}{5} sin (5 x) + C

Solution steps

\int 5 x sin (5 x) d x

Take the constant out:

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

= 5 \cdot \int x sin (5 x) d x

Apply Integration By Parts

: - \frac{1}{5} x cos (5 x) - \int - \frac{1}{5} cos (5 x) d x

= 5 (- \frac{1}{5} x cos (5 x) - \int - \frac{1}{5} cos (5 x) d x)

\int - \frac{1}{5} cos (5 x) d x = - \frac{1}{25} sin (5 x)

= 5 (- \frac{1}{5} x cos (5 x) - (- \frac{1}{25} sin (5 x)))

Simplify

5 (- \frac{1}{5} x cos (5 x) - (- \frac{1}{25} sin (5 x))) : - x cos (5 x) + \frac{1}{5} sin (5 x)

= - x cos (5 x) + \frac{1}{5} sin (5 x)

Add a constant to the solution

= - x cos (5 x) + \frac{1}{5} sin (5 x) + C

\int 7 x^{3} d x

\int \frac{1 - 2 x}{x ^{2} + 9 x + 14} d x

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

\int 2 e^{- x - 2 y} d y

What is the integral of 5xsin(5x) ?
The integral of 5xsin(5x) is -xcos(5x)+1/5 sin(5x)+C