What is the integral of (ln(xy)) ?

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

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integral of (ln(xy))

\int (ln (x y)) d x

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

\frac{d}{d x} (x (a + x)^{2} (a - x)^{3})

18 t^{2} + 9

\frac{d}{d x} (tan (3 x) csc (3 x))

\int 15 (3 x - 7)^{\frac{3}{2}} d x

\frac{d}{d x} (2 e^{x} - 3 x^{e} + e)