What is the integral of-3x^8+4/(x-7) ?

The integral of-3x^8+4/(x-7) is -(x^9)/3+4ln|x-7|+C

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integral of-3x^8+4/(x-7)

\int - 3 x^{8} + \frac{4}{x - 7} d x

- \frac{x ^{9}}{3} + 4 ln ∣ x - 7 ∣ + C

Solution steps

\int - 3 x^{8} + \frac{4}{x - 7} 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 3 x^{8} d x + \int \frac{4}{x - 7} d x

\int 3 x^{8} d x = \frac{x ^{9}}{3}

\int \frac{4}{x - 7} d x = 4 ln ∣ x - 7 ∣

= - \frac{x ^{9}}{3} + 4 ln ∣ x - 7 ∣

Add a constant to the solution

= - \frac{x ^{9}}{3} + 4 ln ∣ x - 7 ∣ + C

What is the integral of-3x^8+4/(x-7) ?
The integral of-3x^8+4/(x-7) is -(x^9)/3+4ln|x-7|+C