What is the integral of (1/(x^{10)}-x^{10}-1/3) ?

The integral of (1/(x^{10)}-x^{10}-1/3) is -1/(9x^9)-(x^{11})/(11)-1/3 x+C

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integral of (1/(x^{10)}-x^{10}-1/3)

\int (\frac{1}{x ^{10}} - x^{10} - \frac{1}{3}) d x

- \frac{1}{9 x ^{9}} - \frac{x ^{11}}{11} - \frac{1}{3} x + C

Solution steps

\int \frac{1}{x ^{10}} - x^{10} - \frac{1}{3} 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 ^{10}} d x - \int x^{10} d x - \int \frac{1}{3} d x

\int \frac{1}{x ^{10}} d x = - \frac{1}{9 x ^{9}}

\int x^{10} d x = \frac{x ^{11}}{11}

\int \frac{1}{3} d x = \frac{1}{3} x

= - \frac{1}{9 x ^{9}} - \frac{x ^{11}}{11} - \frac{1}{3} x

Add a constant to the solution

= - \frac{1}{9 x ^{9}} - \frac{x ^{11}}{11} - \frac{1}{3} x + C

4 t^{3} cos (t)

\int_{- \infty}^{12} r e^{\frac{r}{3}} d r

\frac{\partial}{\partial t} (x y z^{2} tan (y t))

x^{2} + x y - y^{2} = - 9, (3, 6)

\frac{2 x}{1 + x ^{2}}

What is the integral of (1/(x^{10)}-x^{10}-1/3) ?
The integral of (1/(x^{10)}-x^{10}-1/3) is -1/(9x^9)-(x^{11})/(11)-1/3 x+C