What is the integral of 4x^2sin(10x) ?

The integral of 4x^2sin(10x) is 4(-1/10 x^2cos(10x)+1/500 (10xsin(10x)+cos(10x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x^2sin(10x)

\int 4 x^{2} sin (10 x) d x

4 (- \frac{1}{10} x^{2} cos (10 x) + \frac{1}{500} (10 x sin (10 x) + cos (10 x))) + C

Solution steps

\int 4 x^{2} sin (10 x) d x

Take the constant out:

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

= 4 \cdot \int x^{2} sin (10 x) d x

Apply Integration By Parts

: - \frac{1}{10} x^{2} cos (10 x) - \int - \frac{1}{5} x cos (10 x) d x

= 4 (- \frac{1}{10} x^{2} cos (10 x) - \int - \frac{1}{5} x cos (10 x) d x)

\int - \frac{1}{5} x cos (10 x) d x = - \frac{1}{500} (10 x sin (10 x) + cos (10 x))

= 4 (- \frac{1}{10} x^{2} cos (10 x) - (- \frac{1}{500} (10 x sin (10 x) + cos (10 x))))

Simplify

= 4 (- \frac{1}{10} x^{2} cos (10 x) + \frac{1}{500} (10 x sin (10 x) + cos (10 x)))

Add a constant to the solution

= 4 (- \frac{1}{10} x^{2} cos (10 x) + \frac{1}{500} (10 x sin (10 x) + cos (10 x))) + C

\int \frac{1}{( 2 y + 1 ) ( 2 y + 1 ) ^{2} - 9} d y

\int 289 - x^{2} d x

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

\int \frac{2 + 3 x ^{2}}{x ^{3} + 2 x + 10} d x

\int x e^{x} d x

What is the integral of 4x^2sin(10x) ?
The integral of 4x^2sin(10x) is 4(-1/10 x^2cos(10x)+1/500 (10xsin(10x)+cos(10x)))+C