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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

Graph

Popular Examples

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

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

integral of ((3x^2+7x+1)/x)

\int (\frac{3 x ^{2} + 7 x + 1}{x}) d x

integral of 7/(4+(3-x)^2)

\int \frac{7}{4 + ( 3 - x ) ^{2}} d x

integral of (e^x)/(((e^x+1)ln(e^x+1)))

\int \frac{e ^{x}}{( ( e ^{x} + 1 ) ln ( e ^{x} + 1 ) )} d x

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

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