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Popular >

integral of ln(x+2)

Solution

\int ln (x + 2) d x

Solution

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

Solution steps

\int ln (x + 2) 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 + 2

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

5y^'-y=e^{-t}+3t

5 y^{^{'}} - y = e^{- t} + 3 t

integral of ((9sin^3(x)))/(cos(x))

\int \frac{( 9 sin ^{3} ( x ) )}{cos ( x )} d x

limit as x approaches infinity of 1/(5x)

x \to \infty lim (\frac{1}{5 x})

integral of (x*sin(x^2+1))

\int (x \cdot sin (x^{2} + 1)) d x

derivative of e^{(-x^2/2})

\frac{d}{d x} (e^{\frac{- x ^{2}}{2}})

Frequently Asked Questions (FAQ)

What is the integral of ln(x+2) ?
The integral of ln(x+2) is xln(x+2)+2ln(x+2)-x-2+C