What is the integral of (x+3)^2e^x ?

The integral of (x+3)^2e^x is e^xx^2+4e^xx+5e^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+3)^2e^x

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

e^{x} x^{2} + 4 e^{x} x + 5 e^{x} + C

Solution steps

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

Apply Integration By Parts

: (x + 3)^{2} e^{x} - \int 2 (x + 3) e^{x} d x

= (x + 3)^{2} e^{x} - \int 2 (x + 3) e^{x} d x

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

= (x + 3)^{2} e^{x} - 2 (e^{x} x + 2 e^{x})

Simplify

(x + 3)^{2} e^{x} - 2 (e^{x} x + 2 e^{x}) : e^{x} x^{2} + 4 e^{x} x + 5 e^{x}

= e^{x} x^{2} + 4 e^{x} x + 5 e^{x}

Add a constant to the solution

= e^{x} x^{2} + 4 e^{x} x + 5 e^{x} + C

\int e^{6 x^{2}} d x

\int \frac{6 x ^{2} + 3 x - 44}{x ^{2} + x - 6} d x

\int sec^{13} (x) tan (x) d x

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

\int \frac{( ( ln ( x ) ) ^{8} )}{x} d x

What is the integral of (x+3)^2e^x ?
The integral of (x+3)^2e^x is e^xx^2+4e^xx+5e^x+C