What is the integral of (435)/(3x+14)-15 ?

The integral of (435)/(3x+14)-15 is 145ln|3x+14|-15x+C

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integral of (435)/(3x+14)-15

\int \frac{435}{3 x + 14} - 15 d x

145 ln ∣ 3 x + 14 ∣ - 15 x + C

Solution steps

\int \frac{435}{3 x + 14} - 15 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{435}{3 x + 14} d x - \int 15 d x

\int \frac{435}{3 x + 14} d x = 145 ln ∣ 3 x + 14 ∣

\int 15 d x = 15 x

= 145 ln ∣ 3 x + 14 ∣ - 15 x

Add a constant to the solution

= 145 ln ∣ 3 x + 14 ∣ - 15 x + C

f (x) = 3 x^{2} + 2 x, at x = 3

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What is the integral of (435)/(3x+14)-15 ?
The integral of (435)/(3x+14)-15 is 145ln|3x+14|-15x+C