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Popular >

integral of xe^{ln(x)}

Solution

\int x e^{l n (x)} d x

Solution

\frac{x ^{3}}{3} + C

Solution steps

\int x e^{l n (x)} d x

Simplify

x e^{l n (x)} : x^{2}

= \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{3}}{3} + C

Popular Examples

integral of (cot(θ))/(sqrt(sin(θ)))

\int \frac{cot ( θ )}{sin ( θ )} d θ

integral of (5x)/(x^2+6)-1

\int \frac{5 x}{x ^{2} + 6} - 1 d x

integral of (x^2-1)^2(2x)

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

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

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

integral of (3e^x)/(2e^x+7)

\int \frac{3 e ^{x}}{2 e ^{x} + 7} d x

Frequently Asked Questions (FAQ)

What is the integral of xe^{ln(x)} ?
The integral of xe^{ln(x)} is (x^3)/3+C