What is the integral of x^7+1/(x^9) ?

The integral of x^7+1/(x^9) is (x^8)/8-1/(8x^8)+C

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integral of x^7+1/(x^9)

\int x^{7} + \frac{1}{x ^{9}} d x

\frac{x ^{8}}{8} - \frac{1}{8 x ^{8}} + C

Solution steps

\int x^{7} + \frac{1}{x ^{9}} 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^{7} d x + \int \frac{1}{x ^{9}} d x

\int x^{7} d x = \frac{x ^{8}}{8}

\int \frac{1}{x ^{9}} d x = - \frac{1}{8 x ^{8}}

= \frac{x ^{8}}{8} - \frac{1}{8 x ^{8}}

Add a constant to the solution

= \frac{x ^{8}}{8} - \frac{1}{8 x ^{8}} + C

\int (7 x^{4} + x^{2} + 3) d x

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What is the integral of x^7+1/(x^9) ?
The integral of x^7+1/(x^9) is (x^8)/8-1/(8x^8)+C