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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

integral of 1/(x(ln(x))^{7/3)}

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

integral of ((9+x)^2)/(x^2)

\int \frac{( 9 + x ) ^{2}}{x ^{2}} d x

integral of 1/2 x^2\sqrt[5]{x^3-8}

integral of ln^2(z)

\int ln^{2} (z) d z

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

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