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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

y^{\frac{1}{2}} (\frac{d y}{d x}) + y^{\frac{3}{2}} = 1, y (0) = 9

x \to 0 lim (e^{- \frac{2}{x ^{3}}})

f (x) = (x^{3} + 7) e^{x}

\int \frac{2 x}{x ^{2} + 14 x + 49} d x

n = 1 \sum \infty 5 \cdot \frac{2}{n}

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