What is the integral of xln(y) ?

The integral of xln(y) is x(yln(y)-y)+C

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integral of xln(y)

\int x ln (y) d y

x (y ln (y) - y) + C

Solution steps

\int x ln (y) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= x \cdot \int ln (y) d y

Apply Integration By Parts

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

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

\int 1 d y = y

= x (y ln (y) - y)

Add a constant to the solution

= x (y ln (y) - y) + C

x \to \frac{1}{2} lim (\frac{x}{2 x - 1})

f (x) = (x^{3} + 3 x) (2 x + 4)

\int (e^{x}) \cdot cos (n x) d x

\int x x - 10 d x

\frac{3}{s} + \frac{16}{s ( s + 1 )}