What is the integral of 1/2 e^{2x}+1/2 ?

The integral of 1/2 e^{2x}+1/2 is 1/4 e^{2x}+1/2 x+C

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integral of 1/2 e^{2x}+1/2

\int \frac{1}{2} e^{2 x} + \frac{1}{2} d x

\frac{1}{4} e^{2 x} + \frac{1}{2} x + C

Solution steps

\int \frac{1}{2} e^{2 x} + \frac{1}{2} 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 \frac{1}{2} e^{2 x} d x + \int \frac{1}{2} d x

\int \frac{1}{2} e^{2 x} d x = \frac{1}{4} e^{2 x}

\int \frac{1}{2} d x = \frac{1}{2} x

= \frac{1}{4} e^{2 x} + \frac{1}{2} x

Add a constant to the solution

= \frac{1}{4} e^{2 x} + \frac{1}{2} x + C

x^{2} + 1

n = 5 \sum \infty \frac{1}{n + 25}

\frac{d}{d t} (\frac{6}{t})

y^{^{'}} = 3 x (x + 2)^{3}

y^{^{'}} = k y (4000 - y), y (0) = 150

What is the integral of 1/2 e^{2x}+1/2 ?
The integral of 1/2 e^{2x}+1/2 is 1/4 e^{2x}+1/2 x+C