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

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

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

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

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

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

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

= - 2 (- \frac{ln ( x )}{x} - \frac{1}{x})

Add a constant to the solution

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

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

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

\int 4 - ∣ x ∣ d x

\int_{- 1}^{1} x + 1 - 1 d x

\int_{- 3}^{2} ∣ x + 1 ∣ d x

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