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Popular >

integral of e^x+x^e

Solution

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

Solution

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(4-2x)

\int \frac{1}{4 - 2 x} d x

integral of 6xe^{x^3}

\int 6 x e^{x^{3}} d x

integral of 2(x-4)^2

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

integral of (5x^2+7x-2)

\int (5 x^{2} + 7 x - 2) d x

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

\int \frac{2 x + 5}{x ( x ^{2} + 1 )} d x

Frequently Asked Questions (FAQ)

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