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Popular >

integral of 2xex^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

integral of xsqrt(3-2x)

\int x 3 - 2 x d x

integral of x(7-x)^9

\int x (7 - x)^{9} d x

integral of (sec^3(x)+e^{sin(x)})/(sec(x))

\int \frac{sec ^{3} ( x ) + e ^{s i n (x)}}{sec ( x )} d x

integral of (e^{2x}-1)/(e^x)

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

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

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

Frequently Asked Questions (FAQ)

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