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Popular >

integral of ln(xy)

Solution

\int ln (x y) d x

Solution

x ln (y x) - x + C

Solution steps

\int ln (x y) d x

Apply Integration By Parts

: x ln (y x) - \int 1 d x

= x ln (y x) - \int 1 d x

\int 1 d x = x

= x ln (y x) - x

Add a constant to the solution

= x ln (y x) - x + C

Popular Examples

integral from-infinity to 10 of xe^{x/5}

\int_{- \infty}^{10} x e^{\frac{x}{5}} d x

x y^{^{'}} - y + 1 = 0

integral of sqrt(x^2+5x)

\int x^{2} + 5 x d x

(dy)/(dx)+(3x)/(x^2+1)y=(6x)/(x^2+1)

\frac{d y}{d x} + \frac{3 x}{x ^{2} + 1} y = \frac{6 x}{x ^{2} + 1}

derivative of (e^x/2)

\frac{d}{d x} (\frac{e ^{x}}{2})

Frequently Asked Questions (FAQ)

What is the integral of ln(xy) ?
The integral of ln(xy) is xln(yx)-x+C