What is the integral of 1/(sqrt(x))ln(x) ?

The integral of 1/(sqrt(x))ln(x) is 2sqrt(x)ln(x)-4sqrt(x)+C

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integral of 1/(sqrt(x))ln(x)

\int \frac{1}{x} ln (x) d x

2 x ln (x) - 4 x + C

Solution steps

\int \frac{1}{x} ln (x) d x

Simplify

\frac{1}{x} ln (x) : \frac{ln ( x )}{x}

= \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

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What is the integral of 1/(sqrt(x))ln(x) ?
The integral of 1/(sqrt(x))ln(x) is 2sqrt(x)ln(x)-4sqrt(x)+C