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

The integral of (x^2)sin(x) is -x^2cos(x)+2(xsin(x)+cos(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2)sin(x)

integral

(x^{2}) sin (x)

- x^{2} cos (x) + 2 (x sin (x) + cos (x)) + C

Solution steps

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

Apply Integration By Parts

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

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

\int - 2 x cos (x) d x = - 2 (x sin (x) + cos (x))

= - x^{2} cos (x) - (- 2 (x sin (x) + cos (x)))

Simplify

= - x^{2} cos (x) + 2 (x sin (x) + cos (x))

Add a constant to the solution

= - x^{2} cos (x) + 2 (x sin (x) + cos (x)) + C

\frac{e}{( e ^{x} ) ^{2}}

\frac{( 1 + x ) ^{2}}{( x ( 1 + x ^{2} ) )}

\frac{x}{( 4 + 2 x )}

5^{2 x - 7}

y = x^{3} (e^{x})^{4}

What is the integral of (x^2)sin(x) ?
The integral of (x^2)sin(x) is -x^2cos(x)+2(xsin(x)+cos(x))+C