What is the integral of (x^2+5x)cos(x) ?

The integral of (x^2+5x)cos(x) is x^2sin(x)+5xsin(x)+2xcos(x)+5cos(x)-2sin(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+5x)cos(x)

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

x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x) + C

Solution steps

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

Apply Integration By Parts

= (x^{2} + 5 x) sin (x) - \int (2 x + 5) sin (x) d x

\int (2 x + 5) sin (x) d x = - cos (x) (2 x + 5) + 2 sin (x)

= (x^{2} + 5 x) sin (x) - (- cos (x) (2 x + 5) + 2 sin (x))

Simplify

(x^{2} + 5 x) sin (x) - (- cos (x) (2 x + 5) + 2 sin (x)) : x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x)

= x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x)

Add a constant to the solution

= x^{2} sin (x) + 5 x sin (x) + 2 x cos (x) + 5 cos (x) - 2 sin (x) + C

What is the integral of (x^2+5x)cos(x) ?
The integral of (x^2+5x)cos(x) is x^2sin(x)+5xsin(x)+2xcos(x)+5cos(x)-2sin(x)+C