What is the integral of (x^8+18)/(x^7) ?

The integral of (x^8+18)/(x^7) is (x^2)/2-3/(x^6)+C

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integral of (x^8+18)/(x^7)

\int \frac{x ^{8} + 18}{x ^{7}} d x

\frac{x ^{2}}{2} - \frac{3}{x ^{6}} + C

Solution steps

\int \frac{x ^{8} + 18}{x ^{7}} d x

Expand

\frac{x ^{8} + 18}{x ^{7}} : x + \frac{18}{x ^{7}}

= \int x + \frac{18}{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 x d x + \int \frac{18}{x ^{7}} d x

\int x d x = \frac{x ^{2}}{2}

\int \frac{18}{x ^{7}} d x = - \frac{3}{x ^{6}}

= \frac{x ^{2}}{2} - \frac{3}{x ^{6}}

Add a constant to the solution

= \frac{x ^{2}}{2} - \frac{3}{x ^{6}} + C

\int cos (\frac{3}{2} x) d x

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\int \frac{1 - x}{( 1 + x ) ^{2}} d x

What is the integral of (x^8+18)/(x^7) ?
The integral of (x^8+18)/(x^7) is (x^2)/2-3/(x^6)+C