What is the integral of x*sin(5x) ?

The integral of x*sin(5x) is -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 x*sin(5x)

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

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

Solution steps

\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

= - \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)

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

Simplify

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

Add a constant to the solution

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

x \frac{d y}{d x} + y = x^{2} sin (x)

\int_{- π}^{π} sin^{2} (x co) s^{3} x d x

\frac{( x ^{2} + 3 ) d y}{d x} = x y

y = (\frac{t ^{2}}{t ^{3} - 4 t})^{3}

\frac{d y}{d x} = y e^{x}

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