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Popular >

integral of xex^2

Solution

\int x e x^{2} d x

Solution

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

Solution steps

\int x e x^{2} d x

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of (\sqrt[3]{x})/x

integral of (x+7)/x

\int \frac{x + 7}{x} d x

integral of 1/(\sqrt[3]{tan(x))}

integral of x((sin(x))/(cos(x)))^2

\int x (\frac{sin ( x )}{cos ( x )})^{2} d x

integral of 3/(2sqrt(x^3))

\int \frac{3}{2 x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral of xex^2 ?
The integral of xex^2 is (ex^4)/4+C