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Popular Calculus >

integral of e+e^{3x}

Solution

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

Solution

e x + \frac{1}{3} e^{3 x} + C

Solution steps

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

\int e d x = e x

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= e x + \frac{1}{3} e^{3 x}

Add a constant to the solution

= e x + \frac{1}{3} e^{3 x} + C

Graph

Popular Examples

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inverse oflaplace (2e^{-2s})/(s(s+2)(s+3)^2)

limit as x approaches a of 2f(x)-3g(x)

Frequently Asked Questions (FAQ)

What is the integral of e+e^{3x} ?
The integral of e+e^{3x} is ex+1/3 e^{3x}+C