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

The integral of t^2sin(t) is -t^2cos(t)+2(tsin(t)+cos(t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of t^2sin(t)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

f (t) = cos^{2} (\frac{π}{2} - t)

\frac{d}{d x} (2 x^{2} - 5 x + 2)

(x + 2)^{2} y^{^{'}} + 3 (x + 2) y = 4

x \to 0 + lim (1 + x e^{(\frac{2}{x})})

\frac{d y}{d x} = 2 y + y^{5}, y (0) = 1

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