What is the integral of ln(x+17) ?

The integral of ln(x+17) is xln(x+17)+17ln(x+17)-x-17+C

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integral of ln(x+17)

\int ln (x + 17) d x

x ln (x + 17) + 17 ln (x + 17) - x - 17 + C

Solution steps

\int ln (x + 17) d x

Apply u-substitution

: \int ln (u) d u

= \int ln (u) d u

Apply Integration By Parts

: u ln (u) - \int 1 d u

= u ln (u) - \int 1 d u

\int 1 d u = u

= u ln (u) - u

Substitute back

u = x + 17

= (x + 17) ln (x + 17) - (x + 17)

Simplify

(x + 17) ln (x + 17) - (x + 17) : x ln (x + 17) + 17 ln (x + 17) - x - 17

= x ln (x + 17) + 17 ln (x + 17) - x - 17

Add a constant to the solution

= x ln (x + 17) + 17 ln (x + 17) - x - 17 + C

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What is the integral of ln(x+17) ?
The integral of ln(x+17) is xln(x+17)+17ln(x+17)-x-17+C