What is the integral of (2-1/(x^5)+7/(x^3)) ?

The integral of (2-1/(x^5)+7/(x^3)) is 2x+1/(4x^4)-7/(2x^2)+C

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integral of (2-1/(x^5)+7/(x^3))

\int (2 - \frac{1}{x ^{5}} + \frac{7}{x ^{3}}) d x

2 x + \frac{1}{4 x ^{4}} - \frac{7}{2 x ^{2}} + C

Solution steps

\int 2 - \frac{1}{x ^{5}} + \frac{7}{x ^{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 2 d x - \int \frac{1}{x ^{5}} d x + \int \frac{7}{x ^{3}} d x

\int 2 d x = 2 x

\int \frac{1}{x ^{5}} d x = - \frac{1}{4 x ^{4}}

\int \frac{7}{x ^{3}} d x = - \frac{7}{2 x ^{2}}

= 2 x - (- \frac{1}{4 x ^{4}}) - \frac{7}{2 x ^{2}}

Simplify

= 2 x + \frac{1}{4 x ^{4}} - \frac{7}{2 x ^{2}}

Add a constant to the solution

= 2 x + \frac{1}{4 x ^{4}} - \frac{7}{2 x ^{2}} + C

What is the integral of (2-1/(x^5)+7/(x^3)) ?
The integral of (2-1/(x^5)+7/(x^3)) is 2x+1/(4x^4)-7/(2x^2)+C