What is the integral of (1/(x^9)-x^9-1/8) ?

The integral of (1/(x^9)-x^9-1/8) is -1/(8x^8)-(x^{10})/(10)-1/8 x+C

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integral of (1/(x^9)-x^9-1/8)

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

- \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x + C

Solution steps

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

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

\int x^{9} d x = \frac{x ^{10}}{10}

\int \frac{1}{8} d x = \frac{1}{8} x

= - \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x

Add a constant to the solution

= - \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x + C

\frac{x - 5}{x - 25}

\int_{0}^{1} (x^{2} + 1) e^{- 1} d x

\int \frac{5}{1000 + t} d t

\int x^{2} (4 - x) d x

x \to 2 lim (\frac{4 - x ^{2}}{2 + x})

What is the integral of (1/(x^9)-x^9-1/8) ?
The integral of (1/(x^9)-x^9-1/8) is -1/(8x^8)-(x^{10})/(10)-1/8 x+C