What is the integral of (x^6-1/(x^6))^2 ?

The integral of (x^6-1/(x^6))^2 is (x^{13})/(13)-2x-1/(11x^{11)}+C

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integral of (x^6-1/(x^6))^2

\int (x^{6} - \frac{1}{x ^{6}})^{2} d x

\frac{x ^{13}}{13} - 2 x - \frac{1}{11 x ^{11}} + C

Solution steps

\int (x^{6} - \frac{1}{x ^{6}})^{2} d x

Simplify

(x^{6} - \frac{1}{x ^{6}})^{2} : x^{12} - 2 + \frac{1}{x ^{12}}

= \int x^{12} - 2 + \frac{1}{x ^{12}} 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^{12} d x - \int 2 d x + \int \frac{1}{x ^{12}} d x

\int x^{12} d x = \frac{x ^{13}}{13}

\int 2 d x = 2 x

\int \frac{1}{x ^{12}} d x = - \frac{1}{11 x ^{11}}

= \frac{x ^{13}}{13} - 2 x - \frac{1}{11 x ^{11}}

Add a constant to the solution

= \frac{x ^{13}}{13} - 2 x - \frac{1}{11 x ^{11}} + C

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f (t) = 2 t^{4}

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 1})

What is the integral of (x^6-1/(x^6))^2 ?
The integral of (x^6-1/(x^6))^2 is (x^{13})/(13)-2x-1/(11x^{11)}+C