What is the integral of (2+ln(x))/x ?

The integral of (2+ln(x))/x is ((2+ln(x))^2)/2+C

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integral of (2+ln(x))/x

\int \frac{2 + ln ( x )}{x} d x

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

Solution steps

\int \frac{2 + ln ( x )}{x} d x

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = 2 + ln (x)

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

Add a constant to the solution

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

What is the integral of (2+ln(x))/x ?
The integral of (2+ln(x))/x is ((2+ln(x))^2)/2+C