What is the integral of (x^4-6/(x^4)) ?

The integral of (x^4-6/(x^4)) is (x^5)/5+2/(x^3)+C

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integral of (x^4-6/(x^4))

\int (x^{4} - \frac{6}{x ^{4}}) d x

\frac{x ^{5}}{5} + \frac{2}{x ^{3}} + C

Solution steps

\int x^{4} - \frac{6}{x ^{4}} 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^{4} d x - \int \frac{6}{x ^{4}} d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int \frac{6}{x ^{4}} d x = - \frac{2}{x ^{3}}

= \frac{x ^{5}}{5} - (- \frac{2}{x ^{3}})

Simplify

= \frac{x ^{5}}{5} + \frac{2}{x ^{3}}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{2}{x ^{3}} + C

What is the integral of (x^4-6/(x^4)) ?
The integral of (x^4-6/(x^4)) is (x^5)/5+2/(x^3)+C