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

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

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

\frac{1}{2} e^{x} x^{2} - e^{x} x + e^{x} + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{2} e^{x} d x

Apply Integration By Parts

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

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

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

= \frac{1}{2} (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

Simplify

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

= \frac{1}{2} e^{x} x^{2} - e^{x} x + e^{x}

Add a constant to the solution

= \frac{1}{2} e^{x} x^{2} - e^{x} x + e^{x} + C

\int \frac{x + 5}{x ^{2} - 6 x + 3} d x

\int \frac{t}{( 4 - t ^{2} ) ^{\frac{3}{2}}} d t

\int 2 e^{4 z} d z

\int \frac{1}{3 + 2 x} d x

\int \frac{x}{3 x - 10} d x

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