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

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

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

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

2 e^{2 x} + ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 2 e^{2 x} + ln ∣ x ∣

Add a constant to the solution

= 2 e^{2 x} + ln ∣ x ∣ + C

\int \frac{1}{x + 1} d x

\int x^{- 2} \cdot e^{x} d x

\int e^{- (s + 3) t} d t

\int (\frac{3}{x + 1}) d x

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