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Popular Calculus >

integral of x/(x+a)

Solution

\int \frac{x}{x + a} d x

Solution

- a ln ∣ x + a ∣ + x + C

Solution steps

\int \frac{x}{x + a} d x

\frac{x}{x + a} = - \frac{a}{x + a} + 1

= \int - \frac{a}{x + a} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{a}{x + a} d x + \int 1 d x

\int \frac{a}{x + a} d x = a ln ∣ x + a ∣

\int 1 d x = x

= - a ln ∣ x + a ∣ + x

Add a constant to the solution

= - a ln ∣ x + a ∣ + x + C

Graph

Popular Examples

integral of 2tsqrt(3-4t)

\int 2 t 3 - 4 t d t

integral of x^{1/2}-x^2

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

integral of 2xln(x^2+1)

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

integral of xe^{1+x}

\int x e^{1 + x} d x

integral of (5x^2-x+1)/(16x^4-1)

\int \frac{5 x ^{2} - x + 1}{16 x ^{4} - 1} d x

Frequently Asked Questions (FAQ)

What is the integral of x/(x+a) ?
The integral of x/(x+a) is -aln|x+a|+x+C