What is the integral of x^{-4}(x-2)^2 ?

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

integral of x^{-4}(x-2)^2

\int x^{- 4} (x - 2)^{2} d x

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

Solution steps

\int x^{- 4} (x - 2)^{2} d x

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

\int - \frac{2}{81 - 49 x ^{2}} d x

\int \frac{3 x ^{2}}{( 49 + x ^{2} ) ^{2}} d x

\int a^{k x} d x

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

\int \frac{x - 2}{x ^{2} - 6 x} d x

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