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Popular >

integral of (e^x+x)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

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\frac{d}{d x} (lo g_{10} (lo g_{10} (x)))

integral of sin^2(θ)cos(4θ)

\int sin^{2} (θ) cos (4 θ) d θ

sum from n=1 to infinity of (3n!)/(n^n)

n = 1 \sum \infty \frac{3 n !}{n ^{n}}

integral from 0 to pi/2 of sin(2x)

\int_{0}^{\frac{π}{2}} sin (2 x) d x

Frequently Asked Questions (FAQ)

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