What is the integral of (3x^2-1)e^x ?

The integral of (3x^2-1)e^x is 3e^xx^2-6e^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 (3x^2-1)e^x

\int (3 x^{2} - 1) e^{x} d x

3 e^{x} x^{2} - 6 e^{x} x + 5 e^{x} + C

Solution steps

\int (3 x^{2} - 1) e^{x} d x

Apply Integration By Parts

: (3 x^{2} - 1) e^{x} - \int 6 x e^{x} d x

= (3 x^{2} - 1) e^{x} - \int 6 x e^{x} d x

\int 6 x e^{x} d x = 6 (e^{x} x - e^{x})

= (3 x^{2} - 1) e^{x} - 6 (e^{x} x - e^{x})

Simplify

(3 x^{2} - 1) e^{x} - 6 (e^{x} x - e^{x}) : 3 e^{x} x^{2} - 6 e^{x} x + 5 e^{x}

= 3 e^{x} x^{2} - 6 e^{x} x + 5 e^{x}

Add a constant to the solution

= 3 e^{x} x^{2} - 6 e^{x} x + 5 e^{x} + C

\int csc (\frac{a x}{b}) cot (\frac{a x}{b}) d x

\frac{d}{d x} (4 e^{0})

\frac{d}{d t} (- sin (2 t))

sin (\frac{x}{2}), π

\frac{1}{x ^{2} - 1}

What is the integral of (3x^2-1)e^x ?
The integral of (3x^2-1)e^x is 3e^xx^2-6e^xx+5e^x+C