What is the integral of xsin(mx) ?

The integral of xsin(mx) is -1/m xcos(mx)+1/(m^2)sin(mx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of xsin(mx)

\int x sin (m x) d x

- \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x) + C

Solution steps

\int x sin (m x) d x

Apply Integration By Parts

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

\int - \frac{1}{m} cos (m x) d x = - \frac{1}{m ^{2}} sin (m x)

= - \frac{1}{m} x cos (m x) - (- \frac{1}{m ^{2}} sin (m x))

Simplify

= - \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x)

Add a constant to the solution

= - \frac{1}{m} x cos (m x) + \frac{1}{m ^{2}} sin (m x) + C

\int (4 - 16 x) sin (4 x) d x

\int \frac{1}{12 x - 1} d x

\int \frac{x ^{2}}{( 9 + x ^{2} ) ^{\frac{3}{2}}} d x

\int 24 x^{2} arctan (2 x^{3}) d x

\int \frac{1}{1 + 3 cos ^{2} ( x )} d x

What is the integral of xsin(mx) ?
The integral of xsin(mx) is -1/m xcos(mx)+1/(m^2)sin(mx)+C