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Popular >

integral of x^2x^e

Solution

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

Solution

\frac{1}{e + 3} x^{e + 3} + C

Solution steps

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

Simplify

x^{2} x^{e} : x^{2 + e}

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

Apply the Power Rule

: \frac{1}{e + 3} x^{e + 3}

= \frac{1}{e + 3} x^{e + 3}

Add a constant to the solution

= \frac{1}{e + 3} x^{e + 3} + C

Popular Examples

integral of 3^{5x-1}

\int 3^{5 x - 1} d x

\frac{3 d y}{d x} = y^{2}

derivative of (sqrt(x)/(8x+8))

\frac{d}{d x} (\frac{x}{8 x + 8})

limit as x approaches 9 of (x+8)/(x+9)

x \to 9 lim (\frac{x + 8}{x + 9})

limit as p approaches 9 of (sqrt(p)-3)/(sqrt(1+\sqrt{p))-2}

p \to 9 lim (\frac{p - 3}{1 + p - 2})

Frequently Asked Questions (FAQ)

What is the integral of x^2x^e ?
The integral of x^2x^e is 1/(e+3)x^{e+3}+C