What is the integral of (60)/(2x+5)-4 ?

The integral of (60)/(2x+5)-4 is 30ln|2x+5|-4x+C

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integral of (60)/(2x+5)-4

\int \frac{60}{2 x + 5} - 4 d x

30 ln ∣ 2 x + 5 ∣ - 4 x + C

Solution steps

\int \frac{60}{2 x + 5} - 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{60}{2 x + 5} d x - \int 4 d x

\int \frac{60}{2 x + 5} d x = 30 ln ∣ 2 x + 5 ∣

\int 4 d x = 4 x

= 30 ln ∣ 2 x + 5 ∣ - 4 x

Add a constant to the solution

= 30 ln ∣ 2 x + 5 ∣ - 4 x + C

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What is the integral of (60)/(2x+5)-4 ?
The integral of (60)/(2x+5)-4 is 30ln|2x+5|-4x+C