What is the integral of xsin(-3x) ?

The integral of xsin(-3x) is 1/3 xcos(3x)-1/9 sin(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xsin(-3x)

\int x sin (- 3 x) d x

\frac{1}{3} x cos (3 x) - \frac{1}{9} sin (3 x) + C

Solution steps

\int x sin (- 3 x) d x

Apply Integration By Parts

: - \int - \frac{3}{2} x^{2} cos (3 x) d x - \frac{1}{2} x^{2} sin (3 x)

= - \int - \frac{3}{2} x^{2} cos (3 x) d x - \frac{1}{2} x^{2} sin (3 x)

\int - \frac{3}{2} x^{2} cos (3 x) d x = - \frac{1}{18} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x)))

= - (- \frac{1}{18} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x)))) - \frac{1}{2} x^{2} sin (3 x)

Simplify

- (- \frac{1}{18} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x)))) - \frac{1}{2} x^{2} sin (3 x) : \frac{1}{3} x cos (3 x) - \frac{1}{9} sin (3 x)

= \frac{1}{3} x cos (3 x) - \frac{1}{9} sin (3 x)

Add a constant to the solution

= \frac{1}{3} x cos (3 x) - \frac{1}{9} sin (3 x) + C

\int ln (x^{2} + 1) d x

e^{2 t} sin (5 t)

\frac{4 - 3 x - x ^{2}}{x ^{2} - 6}

\int_{0}^{\frac{π}{2}} - 2 sin^{2} (3 x) d x

(\frac{d y}{d x}) = 0.011 \cdot y \cdot (2 - (y - 25))

What is the integral of xsin(-3x) ?
The integral of xsin(-3x) is 1/3 xcos(3x)-1/9 sin(3x)+C