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

The integral of ((2-x)/x)^2 is -4/x-4ln|x|+x+C

Popular >

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

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

- \frac{4}{x} - 4 ln ∣ x ∣ + x + C

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Expand

\frac{( 2 - x ) ^{2}}{x ^{2}} : \frac{4}{x ^{2}} - \frac{4}{x} + 1

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

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int 1 d x = x

= - \frac{4}{x} - 4 ln ∣ x ∣ + x

Add a constant to the solution

= - \frac{4}{x} - 4 ln ∣ x ∣ + x + C

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

\int z z - 8 d z

3 x

\int \frac{x ^{2}}{( 4 - x ^{2} ) ^{3}} d x

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

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