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

The integral of (sqrt(1+ln(x)))/x is 2/3 (1+ln(x))^{3/2}+C

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

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

\frac{2}{3} (1 + ln (x))^{\frac{3}{2}} + C

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 + ln (x)

= \frac{2}{3} (1 + ln (x))^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (1 + ln (x))^{\frac{3}{2}} + C

3 t^{2} + 25

x \to - 4 - lim (\frac{1}{x ^{2} - 16})

\frac{\partial}{\partial x} (1 + x^{2} + y^{2})

\frac{d}{d x} (e^{- \frac{x}{t}})

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

What is the integral of (sqrt(1+ln(x)))/x ?
The integral of (sqrt(1+ln(x)))/x is 2/3 (1+ln(x))^{3/2}+C