What is the integral of (3x^2-4x+2)e^x ?

The integral of (3x^2-4x+2)e^x is 3e^xx^2-10e^xx+12e^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^2-4x+2)e^x

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

3 e^{x} x^{2} - 10 e^{x} x + 12 e^{x} + C

Solution steps

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

Expand

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

= \int 3 e^{x} x^{2} - 4 e^{x} x + 2 e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 e^{x} x^{2} d x - \int 4 e^{x} x d x + \int 2 e^{x} d x

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

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

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

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

Simplify

3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) - 4 (e^{x} x - e^{x}) + 2 e^{x} : 3 e^{x} x^{2} - 10 e^{x} x + 12 e^{x}

= 3 e^{x} x^{2} - 10 e^{x} x + 12 e^{x}

Add a constant to the solution

= 3 e^{x} x^{2} - 10 e^{x} x + 12 e^{x} + C

\int \frac{1}{x ^{2} - 4 x - 21} d x

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

\int \frac{5}{e ^{4 x}} d x

\int \frac{x - 76}{x ^{2} ( x + 4 )} d x

\int \frac{tan ^{4} ( x )}{cos ^{4} ( x )} d x

What is the integral of (3x^2-4x+2)e^x ?
The integral of (3x^2-4x+2)e^x is 3e^xx^2-10e^xx+12e^x+C