en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2e^2x

Solution

integral

x^{2} e^{2} x

Solution

\frac{e ^{2} x ^{4}}{4} + C

Solution steps

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

Take the constant out:

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

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

Simplify

x^{2} x : x^{3}

= e^{2} \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= e^{2} \frac{x ^{4}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{2} x ^{4}}{4}

Add a constant to the solution

= \frac{e ^{2} x ^{4}}{4} + C

Graph

Popular Examples

integral of 3/(x^4)integral

\frac{3}{x ^{4}}

integral of (e^x)/(x^4)integral

\frac{e ^{x}}{x ^{4}}

integral of (tan(x))/(1+cos^4(x))integral

\frac{tan ( x )}{1 + cos ^{4} ( x )}

integral of (2x)/((x+y)^3)integral

\frac{2 x}{( x + y ) ^{3}}

integral of 2/((x+1)^2)integral

\frac{2}{( x + 1 ) ^{2}}

Frequently Asked Questions (FAQ)

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