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

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

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integral of ln(sqrt(x))

\int ln (x) d x

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

Solution steps

\int ln (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

ln (x) : \frac{1}{2} ln (x)

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

Add a constant to the solution

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

\int \frac{5 e ^{x}}{e ^{2 x} + 10 e ^{x} + 25} d x

x \to 2 lim (- (x))

y^{^{''}} = t

d y - (y - 4) 2 d x = 0

\int_{2}^{4} (x^{3} + 4) d x

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