What is the integral of (x+1)^2e^x ?

The integral of (x+1)^2e^x is e^xx^2+e^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+1)^2e^x

\int (x + 1)^{2} e^{x} d x

e^{x} x^{2} + e^{x} + C

Solution steps

\int (x + 1)^{2} e^{x} d x

Apply Integration By Parts

: (x + 1)^{2} e^{x} - \int 2 (x + 1) e^{x} d x

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

\int 2 (x + 1) e^{x} d x = 2 e^{x} x

= (x + 1)^{2} e^{x} - 2 e^{x} x

Simplify

(x + 1)^{2} e^{x} - 2 e^{x} x : e^{x} x^{2} + e^{x}

= e^{x} x^{2} + e^{x}

Add a constant to the solution

= e^{x} x^{2} + e^{x} + C

\int \frac{1}{2 x + 4} d x

\frac{d}{d x} (ln (ln (x^{2 x})))

\int \frac{27}{x ( x ^{2} + 4 ) ^{2}} d x

\frac{d y}{d x} = ln (x^{y})

\int (x^{4} - 4^{x} + 4 x - \frac{4}{x}) d x