What is the integral of ln(y)cos(y) ?

The integral of ln(y)cos(y) is ln(y)sin(y)-\Si(y)+C

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integral of ln(y)cos(y)

\int ln (y) cos (y) d y

ln (y) sin (y) - Si (y) + C

Solution steps

\int ln (y) cos (y) d y

Apply Integration By Parts

= ln (y) sin (y) - \int \frac{sin ( y )}{y} d y

\int \frac{sin ( y )}{y} d y = Si (y)

= ln (y) sin (y) - Si (y)

Add a constant to the solution

= ln (y) sin (y) - Si (y) + C

What is the integral of ln(y)cos(y) ?
The integral of ln(y)cos(y) is ln(y)sin(y)-\Si(y)+C