What is the integral of (log_{e}(x))/(sqrt(x)) ?

The integral of (log_{e}(x))/(sqrt(x)) is 2sqrt(x)ln(x)-4sqrt(x)+C

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integral of (log_{e}(x))/(sqrt(x))

\int \frac{lo g _{e} ( x )}{x} d x

2 x ln (x) - 4 x + C

Solution steps

\int \frac{lo g _{e} ( x )}{x} d x

Simplify

lo g_{e} (x) : ln (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

\frac{\partial}{\partial x} (17 - x^{2} - y^{2})

\frac{d}{d x} (\frac{3}{8 ( 1 + x ) ^{\frac{5}{2}}})

n = 1 \sum \infty \frac{5}{1 0 ^{n}}

y = 14 x

\int 12 tan^{11} (x) sec^{2} (x) d x

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