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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

derivative of f(x)=(2x^2+4x+2)/(sqrt(x))derivative of

f (x) = \frac{2 x ^{2} + 4 x + 2}{x}

(\partial)/(\partial x)(y+3xy^2-18)

\frac{\partial}{\partial x} (y + 3 x y^{2} - 18)

tangent of f(x)=sin(x),\at x=(7pi)/6 tangent of

f (x) = sin (x), at x = \frac{7 π}{6}

limit as x approaches 2 of (8-x^3)/(x^2-2x)

x \to 2 lim (\frac{8 - x ^{3}}{x ^{2} - 2 x})

limit as x approaches infinity of (1-x\sqrt[x]{x})/(x-sin(x))

Frequently Asked Questions (FAQ)

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