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

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

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

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

30 ln ∣ 2 x + 5 ∣ - 5 x + C

Solution steps

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

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

\int 5 d x = 5 x

= 30 ln ∣ 2 x + 5 ∣ - 5 x

Add a constant to the solution

= 30 ln ∣ 2 x + 5 ∣ - 5 x + C

\int cot (x) (- 8 sin (x) - 10 csc (x)) d x

y^{2} + x^{2} y^{^{'}} = 0

\int x (x + 2)^{- \frac{3}{2}} d x

\int e^{c o s (4 x)} sin (4 x) d x

\frac{5}{r ^{3}}

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