What is the integral of 2xsin(5x) ?

The integral of 2xsin(5x) is 2(-1/5 xcos(5x)+1/25 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 2xsin(5x)

\int 2 x sin (5 x) d x

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

Solution steps

\int 2 x sin (5 x) d x

Take the constant out:

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

= 2 \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

= 2 (- \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)

= 2 (- \frac{1}{5} x cos (5 x) - (- \frac{1}{25} sin (5 x)))

Simplify

= 2 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x))

Add a constant to the solution

= 2 (- \frac{1}{5} x cos (5 x) + \frac{1}{25} sin (5 x)) + C

\int \frac{θ ^{2}}{θ ^{2} + 5} d θ

\int x (x + 7)^{7} d x

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

\int 2 x cot (1 - 3 x^{2}) d x

\int \frac{4 x}{x} d x

What is the integral of 2xsin(5x) ?
The integral of 2xsin(5x) is 2(-1/5 xcos(5x)+1/25 sin(5x))+C