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Popular >

integral of ln(x+a)

Solution

\int ln (x + a) d x

Solution

x ln (x + a) + a ln (x + a) - x - a + C

Solution steps

\int ln (x + a) 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 + a

= (x + a) ln (x + a) - (x + a)

Simplify

(x + a) ln (x + a) - (x + a) : x ln (x + a) + a ln (x + a) - x - a

= x ln (x + a) + a ln (x + a) - x - a

Add a constant to the solution

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

Popular Examples

integral of 5+sec^2(x)

\int 5 + sec^{2} (x) d x

integral of sin^3(x/2)cos^7(x/2)

\int sin^{3} (\frac{x}{2}) cos^{7} (\frac{x}{2}) d x

integral of (ln(x^2+1))

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

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

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

integral of ((1+tan(x))^2)/(cos^2(x))

\int \frac{( 1 + tan ( x ) ) ^{2}}{cos ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

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