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Popular >

integral of x/(a+x)

Solution

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

Solution

- a ln ∣ a + x ∣ + x + C

Solution steps

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

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

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

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

\int 1 d x = x

= - a ln ∣ a + x ∣ + x

Add a constant to the solution

= - a ln ∣ a + x ∣ + x + C

Popular Examples

integral of 1/(sqrt(9+\sqrt{4+x))}

\int \frac{1}{9 + 4 + x} d x

integral of (2x^2+1)

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

integral of arctan((x^2)^2)x^2)^2

\int arctan ((x^{2})^{2}) d (x^{2})^{2}

integral of cotan^2(x/4)

\int co tan^{2} (\frac{x}{4}) d x

integral of (1/x+3/(x^2))

\int (\frac{1}{x} + \frac{3}{x ^{2}}) d x

Frequently Asked Questions (FAQ)

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