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Popular >

integral of 1/(x-y)

Solution

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

Solution

ln ∣ - y + x ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = - y + x

= ln ∣ - y + x ∣

Add a constant to the solution

= ln ∣ - y + x ∣ + C

Popular Examples

integral from-1 to 1 of (13-12u)^{-1}

\int_{- 1}^{1} (13 - 12 u)^{- 1} d u

limit as x approaches-3 of 4

x \to - 3 lim (4)

(\partial)/(\partial x)(x^4+3^y+x^y)

\frac{\partial}{\partial x} (x^{4} + 3^{y} + x^{y})

limit as h approaches 0 of 3x^2-2xh+5h

h \to 0 lim (3 x^{2} - 2 x h + 5 h)

tangent of 2e^xcos(x)(0.2)tangent of

2 e^{x} cos (x) (0.2)

Frequently Asked Questions (FAQ)

What is the integral of 1/(x-y) ?
The integral of 1/(x-y) is ln|-y+x|+C