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Popular Calculus >

integral of x^3ln(e^x)

Solution

\int x^{3} ln (e^{x}) d x

Solution

\frac{x ^{5}}{5} + C

Solution steps

\int x^{3} ln (e^{x}) d x

Simplify

x^{3} ln (e^{x}) : x^{4}

= \int x^{4} d x

Apply the Power Rule

= \frac{x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{5}}{5} + C

Graph

Popular Examples

integral of (3x^2+5x+4)/(x^3+x^2+x-3)

\int \frac{3 x ^{2} + 5 x + 4}{x ^{3} + x ^{2} + x - 3} d x

integral of (9x)/(sqrt(2+15x))

\int \frac{9 x}{2 + 15 x} d x

integral of sin(1-2x)sin(2x+3)

\int sin (1 - 2 x) sin (2 x + 3) d x

integral of ((y+4))/(y^2+16)

\int \frac{( y + 4 )}{y ^{2} + 16} d y

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

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

Frequently Asked Questions (FAQ)

What is the integral of x^3ln(e^x) ?
The integral of x^3ln(e^x) is (x^5)/5+C