What is the integral of ex^{e+1} ?

The integral of ex^{e+1} is e/(e+2)x^{e+2}+C

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integral of ex^{e+1}

\int e x^{e + 1} d x

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

Solution steps

\int e x^{e + 1} d x

Take the constant out:

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

= e \cdot \int x^{e + 1} d x

Apply the Power Rule

: \frac{1}{e + 2} x^{e + 2}

= e \frac{1}{e + 2} x^{e + 2}

Simplify

e \frac{1}{e + 2} x^{e + 2} : \frac{e}{e + 2} x^{e + 2}

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

Add a constant to the solution

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

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