What is the integral of (e^{4x}+4/(3x-5)) ?

The integral of (e^{4x}+4/(3x-5)) is 1/4 e^{4x}+4/3 ln|3x-5|+C

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integral of (e^{4x}+4/(3x-5))

\int (e^{4 x} + \frac{4}{3 x - 5}) d x

\frac{1}{4} e^{4 x} + \frac{4}{3} ln ∣ 3 x - 5 ∣ + C

Solution steps

\int e^{4 x} + \frac{4}{3 x - 5} 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^{4 x} d x + \int \frac{4}{3 x - 5} d x

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

\int \frac{4}{3 x - 5} d x = \frac{4}{3} ln ∣ 3 x - 5 ∣

= \frac{1}{4} e^{4 x} + \frac{4}{3} ln ∣ 3 x - 5 ∣

Add a constant to the solution

= \frac{1}{4} e^{4 x} + \frac{4}{3} ln ∣ 3 x - 5 ∣ + C

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What is the integral of (e^{4x}+4/(3x-5)) ?
The integral of (e^{4x}+4/(3x-5)) is 1/4 e^{4x}+4/3 ln|3x-5|+C