What is the integral of (x^2-1)sin(x) ?

The integral of (x^2-1)sin(x) is -x^2cos(x)+2xsin(x)+3cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x^2-1)sin(x)

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

- x^{2} cos (x) + 2 x sin (x) + 3 cos (x) + C

Solution steps

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

Apply Integration By Parts

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

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

= - cos (x) (x^{2} - 1) - (- 2 (x sin (x) + cos (x)))

Simplify

- cos (x) (x^{2} - 1) - (- 2 (x sin (x) + cos (x))) : - x^{2} cos (x) + 2 x sin (x) + 3 cos (x)

= - x^{2} cos (x) + 2 x sin (x) + 3 cos (x)

Add a constant to the solution

= - x^{2} cos (x) + 2 x sin (x) + 3 cos (x) + C

\int y^{3} y^{4} + 5 d y

\int (x^{7} + 2 x)^{5} d x

\int e^{x^{a}} d x

\int (\frac{x}{x + 3}) d x

\int y e^{x} cos (yz) d z

What is the integral of (x^2-1)sin(x) ?
The integral of (x^2-1)sin(x) is -x^2cos(x)+2xsin(x)+3cos(x)+C