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

The integral of ((ln(x)+1))/x is ((ln(x)+1)^2)/2+C

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

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = ln (x) + 1

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

Add a constant to the solution

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

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