What is the integral of 5x^2sin(8x) ?

The integral of 5x^2sin(8x) is 5(-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5x^2sin(8x)

\int 5 x^{2} sin (8 x) d x

5 (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))) + C

Solution steps

\int 5 x^{2} sin (8 x) d x

Take the constant out:

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

= 5 \cdot \int x^{2} sin (8 x) d x

Apply Integration By Parts

: - \frac{1}{8} x^{2} cos (8 x) - \int - \frac{1}{4} x cos (8 x) d x

= 5 (- \frac{1}{8} x^{2} cos (8 x) - \int - \frac{1}{4} x cos (8 x) d x)

\int - \frac{1}{4} x cos (8 x) d x = - \frac{1}{256} (8 x sin (8 x) + cos (8 x))

= 5 (- \frac{1}{8} x^{2} cos (8 x) - (- \frac{1}{256} (8 x sin (8 x) + cos (8 x))))

Simplify

= 5 (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)))

Add a constant to the solution

= 5 (- \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x))) + C

\frac{\partial}{\partial x} (6 x y^{3} z^{3} + 7 x yz)

\frac{d y}{d x} = 0.75 y

\frac{d y}{d x} + 6 x y^{4} = 0

\frac{d r}{d θ} = \frac{r ^{2}}{θ}, r (1) = 2

What is the integral of 5x^2sin(8x) ?
The integral of 5x^2sin(8x) is 5(-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x)))+C