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Popular >

integral of x+e^x

Solution

\int x + e^{x} d x

Solution

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

Solution steps

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

\int x d x = \frac{x ^{2}}{2}

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches infinity of (1+sin(6x))^{1/(3x)}

x \to \infty lim ((1 + sin (6 x))^{\frac{1}{3 x}})

limit as x approaches 1 of x*ln(x)

x \to 1 lim (x \cdot ln (x))

limit as t approaches infinity of (1-e^{-2t})/t

t \to \infty lim (\frac{1 - e ^{- 2 t}}{t})

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

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

derivative of arctan(e^{-x})

\frac{d}{d x} (arctan (e^{- x}))

Frequently Asked Questions (FAQ)

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