What is the integral of ln(x+9) ?

The integral of ln(x+9) is xln(x+9)+9ln(x+9)-x-9+C

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integral of ln(x+9)

\int ln (x + 9) d x

x ln (x + 9) + 9 ln (x + 9) - x - 9 + C

Solution steps

\int ln (x + 9) 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 + 9

= (x + 9) ln (x + 9) - (x + 9)

Simplify

(x + 9) ln (x + 9) - (x + 9) : x ln (x + 9) + 9 ln (x + 9) - x - 9

= x ln (x + 9) + 9 ln (x + 9) - x - 9

Add a constant to the solution

= x ln (x + 9) + 9 ln (x + 9) - x - 9 + C

\int e^{2} d x

\frac{d}{d x} ((9 x + 8) x^{2})

y^{^{'}} = (1 - 2 x) y^{2}, y (0) = - \frac{1}{6}

\frac{d}{d x} (x^{3} y^{5} - 2 x^{2} y + x)

\int (x - 2) (x + 2) d x

What is the integral of ln(x+9) ?
The integral of ln(x+9) is xln(x+9)+9ln(x+9)-x-9+C