What is the integral of ln(x)y ?

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

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integral of ln(x)y

\int ln (x) y d x

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

Solution steps

\int ln (x) y d x

Take the constant out:

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

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

Apply Integration By Parts

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

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

\int 1 d x = x

= y (x ln (x) - x)

Add a constant to the solution

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

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