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

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

Popular >

integral of (x-1/x)^2

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

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

Solution steps

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

Expand

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

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

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

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

y^{^{'}} = (x - 5) e^{- 2 y}

\int_{1}^{2} \frac{v ^{4} + 5 v ^{7}}{v ^{3}} d v

- t^{2} δ (t - 2)

\int x^{5} x^{3} + 1 d x

\int (4 x^{2} + 3 x) cos (x) d x

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