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

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

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integral of 2+1/(x^2)-3/(x^4)

integral

2 + \frac{1}{x ^{2}} - \frac{3}{x ^{4}}

2 x - \frac{1}{x} + \frac{1}{x ^{3}} + C

Solution steps

\int 2 + \frac{1}{x ^{2}} - \frac{3}{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 2 d x + \int \frac{1}{x ^{2}} d x - \int \frac{3}{x ^{4}} d x

\int 2 d x = 2 x

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

\int \frac{3}{x ^{4}} d x = - \frac{1}{x ^{3}}

= 2 x - \frac{1}{x} - (- \frac{1}{x ^{3}})

Simplify

= 2 x - \frac{1}{x} + \frac{1}{x ^{3}}

Add a constant to the solution

= 2 x - \frac{1}{x} + \frac{1}{x ^{3}} + C

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