What is the integral of ln(x+7) ?

The integral of ln(x+7) is xln(x+7)+7ln(x+7)-x-7+C

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integral of ln(x+7)

\int ln (x + 7) d x

x ln (x + 7) + 7 ln (x + 7) - x - 7 + C

Solution steps

\int ln (x + 7) 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 + 7

= (x + 7) ln (x + 7) - (x + 7)

Simplify

(x + 7) ln (x + 7) - (x + 7) : x ln (x + 7) + 7 ln (x + 7) - x - 7

= x ln (x + 7) + 7 ln (x + 7) - x - 7

Add a constant to the solution

= x ln (x + 7) + 7 ln (x + 7) - x - 7 + C

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What is the integral of ln(x+7) ?
The integral of ln(x+7) is xln(x+7)+7ln(x+7)-x-7+C