What is the integral of (3/(2x-1)+5/(3x-4)) ?

The integral of (3/(2x-1)+5/(3x-4)) is 3/2 ln|2x-1|+5/3 ln|3x-4|+C

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integral of (3/(2x-1)+5/(3x-4))

\int (\frac{3}{2 x - 1} + \frac{5}{3 x - 4}) d x

\frac{3}{2} ln ∣ 2 x - 1 ∣ + \frac{5}{3} ln ∣ 3 x - 4 ∣ + C

Solution steps

\int \frac{3}{2 x - 1} + \frac{5}{3 x - 4} 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{3}{2 x - 1} d x + \int \frac{5}{3 x - 4} d x

\int \frac{3}{2 x - 1} d x = \frac{3}{2} ln ∣ 2 x - 1 ∣

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

= \frac{3}{2} ln ∣ 2 x - 1 ∣ + \frac{5}{3} ln ∣ 3 x - 4 ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ 2 x - 1 ∣ + \frac{5}{3} ln ∣ 3 x - 4 ∣ + C

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What is the integral of (3/(2x-1)+5/(3x-4)) ?
The integral of (3/(2x-1)+5/(3x-4)) is 3/2 ln|2x-1|+5/3 ln|3x-4|+C