What is the integral of 4t^2e^t ?

The integral of 4t^2e^t is 4(t^2e^t-2(e^tt-e^t))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4t^2e^t

\int 4 t^{2} e^{t} d t

4 (t^{2} e^{t} - 2 (e^{t} t - e^{t})) + C

Solution steps

\int 4 t^{2} e^{t} d t

Take the constant out:

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

= 4 \cdot \int t^{2} e^{t} d t

Apply Integration By Parts

: t^{2} e^{t} - \int 2 t e^{t} d t

= 4 (t^{2} e^{t} - \int 2 t e^{t} d t)

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

= 4 (t^{2} e^{t} - 2 (e^{t} t - e^{t}))

Add a constant to the solution

= 4 (t^{2} e^{t} - 2 (e^{t} t - e^{t})) + C

\int (3 - 2 x) e^{5 - 4 x} d x

\int (2 x - 1)^{10} d x

\int x (3 x + 2)^{5} d x

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

\int \frac{e ^{x + 3}}{x} d x

What is the integral of 4t^2e^t ?
The integral of 4t^2e^t is 4(t^2e^t-2(e^tt-e^t))+C