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

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

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integral of cos(x)(ln(x))

\int cos (x) (ln (x)) d x

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

Solution steps

\int cos (x) ln (x) d x

Apply Integration By Parts

: ln (x) sin (x) - \int \frac{sin ( x )}{x} d x

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

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

= ln (x) sin (x) - Si (x)

Add a constant to the solution

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

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