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

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

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integral of-1+ln(x)

\int - 1 + ln (x) d x

- 2 x + x ln (x) + C

Solution steps

\int - 1 + ln (x) d x

Apply Integration By Parts

: x (- 1 + ln (x)) - \int 1 d x

= x (- 1 + ln (x)) - \int 1 d x

\int 1 d x = x

= x (- 1 + ln (x)) - x

Simplify

x (- 1 + ln (x)) - x : - 2 x + x ln (x)

= - 2 x + x ln (x)

Add a constant to the solution

= - 2 x + x ln (x) + C

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