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

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

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integral of ((x-2)(x+2))/(x^2)

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

- \frac{( x - 2 ) ( x + 2 )}{x} + 2 x + C

Solution steps

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

Apply Integration By Parts

: - \frac{( x - 2 ) ( x + 2 )}{x} - \int - 2 d x

= - \frac{( x - 2 ) ( x + 2 )}{x} - \int - 2 d x

\int - 2 d x = - 2 x

= - \frac{( x - 2 ) ( x + 2 )}{x} - (- 2 x)

Simplify

= - \frac{( x - 2 ) ( x + 2 )}{x} + 2 x

Add a constant to the solution

= - \frac{( x - 2 ) ( x + 2 )}{x} + 2 x + C

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