What is the integral of x^3sin(3x) ?

The integral of x^3sin(3x) is -1/3 x^3cos(3x)+1/27 (9x^2sin(3x)-2(-3xcos(3x)+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 x^3sin(3x)

\int x^{3} sin (3 x) d x

- \frac{1}{3} x^{3} cos (3 x) + \frac{1}{27} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x))) + C

Solution steps

\int x^{3} sin (3 x) d x

Apply Integration By Parts

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

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

\int - x^{2} cos (3 x) d x = - \frac{1}{27} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x)))

= - \frac{1}{3} x^{3} cos (3 x) - (- \frac{1}{27} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x))))

Simplify

= - \frac{1}{3} x^{3} cos (3 x) + \frac{1}{27} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x)))

Add a constant to the solution

= - \frac{1}{3} x^{3} cos (3 x) + \frac{1}{27} (9 x^{2} sin (3 x) - 2 (- 3 x cos (3 x) + sin (3 x))) + C

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

\frac{5 s}{s ^{2} ( s ^{2} + 16 )}

n = 0 \sum \infty n sin (\frac{1}{n})

y = 3 x^{3} - 3 x, (1, 0)

x \to 2 lim (x^{2} - 4 x + 3)

What is the integral of x^3sin(3x) ?
The integral of x^3sin(3x) is -1/3 x^3cos(3x)+1/27 (9x^2sin(3x)-2(-3xcos(3x)+sin(3x)))+C