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Popular >

integral of x/(x+y)

Solution

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

Solution

- y ln ∣ y + x ∣ + x + C

Solution steps

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

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

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

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

\int 1 d x = x

= - y ln ∣ y + x ∣ + x

Add a constant to the solution

= - y ln ∣ y + x ∣ + x + C

Graph

Popular Examples

implicit (dy)/(dx),y^2=12x implicit derivative

\frac{d y}{d x}, y^{2} = 12 x

integral of 2xe-2x

\int 2 x e - 2 x d x

integral of x^2+y

\int x^{2} + y d x

derivative of y=(x-1)^3(x+2)^4 derivative of

y = (x - 1)^{3} (x + 2)^{4}

derivative of y=cot^2(pix)derivative of

y = cot^{2} (π x)

Frequently Asked Questions (FAQ)

What is the integral of x/(x+y) ?
The integral of x/(x+y) is -yln|y+x|+x+C