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Popular >

integral of x^e+e^x

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(cos(y^2))

\frac{\partial}{\partial x} (cos (y^{2}))

integral of 64x^3(4x^2+1)^3

\int 64 x^{3} (4 x^{2} + 1)^{3} d x

integral of x^2(x^3+2)^5

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

derivative of (cot^2(2x)/(1+x^2))

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

derivative of 2x(x+5)derivative of

2 x (x + 5)

Frequently Asked Questions (FAQ)

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