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Popular >

integral of ln(a+x)

Solution

\int ln (a + x) d x

Solution

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

Solution steps

\int ln (a + x) 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 = a + x

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

Simplify

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of 6tan(x)sec^5(x)

\int 6 tan (x) sec^{5} (x) d x

integral of (y^{1/3})/((y^{4/3)+9)^2}

\int \frac{y ^{\frac{1}{3}}}{( y ^{\frac{4}{3}} + 9 ) ^{2}} d y

integral of (4x^5)/(sqrt(4+x^2))

\int \frac{4 x ^{5}}{4 + x ^{2}} d x

integral of 1/(xsqrt(11+x^2))

\int \frac{1}{x 11 + x ^{2}} d x

integral of (4x)/(4x-2)

\int \frac{4 x}{4 x - 2} d x

Frequently Asked Questions (FAQ)

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