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

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

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

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

2 x ln (x) - 4 x + C

Solution steps

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

Simplify

\frac{x ln ( x )}{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 (sqrt(x)ln(x))/x ?
The integral of (sqrt(x)ln(x))/x is 2sqrt(x)ln(x)-4sqrt(x)+C