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Popular >

integral of xe^4x

Solution

\int x e^{4} x d x

Solution

\frac{e ^{4} x ^{3}}{3} + C

Solution steps

\int x e^{4} x d x

Take the constant out:

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

= e^{4} \cdot \int xx d x

Simplify

xx : x^{2}

= e^{4} \cdot \int x^{2} d x

Apply the Power Rule

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

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

Multiply fractions:

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

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

Add a constant to the solution

= \frac{e ^{4} x ^{3}}{3} + C

Graph

Popular Examples

integral of 1/(x^2+x+3)

\int \frac{1}{x ^{2} + x + 3} d x

integral of x/(5+x^4)

\int \frac{x}{5 + x ^{4}} d x

integral of 1/(3sec(x))

\int \frac{1}{3 sec ( x )} d x

integral of (3-4x)(-x-5)

\int (3 - 4 x) (- x - 5) d x

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

\int x (3 x^{2} - 4)^{5} d x

Frequently Asked Questions (FAQ)

What is the integral of xe^4x ?
The integral of xe^4x is (e^4x^3)/3+C