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Popular >

integral of (x+3e^x)

Solution

\int (x + 3 e^{x}) d x

Solution

\frac{x ^{2}}{2} + 3 e^{x} + C

Solution steps

\int x + 3 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 3 e^{x} d x

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

\int 3 e^{x} d x = 3 e^{x}

= \frac{x ^{2}}{2} + 3 e^{x}

Add a constant to the solution

= \frac{x ^{2}}{2} + 3 e^{x} + C

Graph

Popular Examples

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\int \frac{x}{1 - 25 x ^{2}} d x

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\int 7 x sin (x^{2}) d x

integral of sqrt(tan(x))*sec^2(x)

\int tan (x) \cdot sec^{2} (x) d x

Frequently Asked Questions (FAQ)

What is the integral of (x+3e^x) ?
The integral of (x+3e^x) is (x^2)/2+3e^x+C