What is the integral of (ln(x))/(sqrt(x)) ?

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

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integral of (ln(x))/(sqrt(x))

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

2 x ln (x) - 4 x + C

Solution steps

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

Apply Integration By Parts

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

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

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

= 2 x ln (x) - 4 x

Add a constant to the solution

= 2 x ln (x) - 4 x + C

\int \frac{1}{t - 1} d t

\frac{d}{d x} ((4 x - 21) ln ((2 x - 11) (x - 5)))

\frac{2}{x ^{2}}, 2

\int \frac{x ^{2} - 18 x - 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

(x + y)^{2} d x + (2 x y + x^{2} - 1) d y = 0, y (1) = 1

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