What is the integral of ln(x+5) ?

The integral of ln(x+5) is xln(x+5)+5ln(x+5)-x-5+C

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integral of ln(x+5)

\int ln (x + 5) d x

x ln (x + 5) + 5 ln (x + 5) - x - 5 + C

Solution steps

\int ln (x + 5) d x

Apply u-substitution

= \int ln (u) d u

Apply Integration By Parts

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

\int 1 d u = u

= u ln (u) - u

Substitute back

u = x + 5

= (x + 5) ln (x + 5) - (x + 5)

Simplify

(x + 5) ln (x + 5) - (x + 5) : x ln (x + 5) + 5 ln (x + 5) - x - 5

= x ln (x + 5) + 5 ln (x + 5) - x - 5

Add a constant to the solution

= x ln (x + 5) + 5 ln (x + 5) - x - 5 + C

\int_{0}^{1} \frac{4}{( x + 1 ) ( x ^{2} + 1 )} d x

\int (\frac{1}{( 1 - x ) ^{2}}) d x

\int 2 t + 5 d t

\int \frac{2 x}{x ^{2} + y ^{2}} d y

\frac{d}{d x} (7 x^{3} + 4)

What is the integral of ln(x+5) ?
The integral of ln(x+5) is xln(x+5)+5ln(x+5)-x-5+C