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

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

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integral of (ln(x))(sin(x))

\int (ln (x)) (sin (x)) d x

- ln (x) cos (x) + Ci (x) + C

Solution steps

\int ln (x) sin (x) d x

Apply Integration By Parts

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

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

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - ln (x) cos (x) - (- Ci (x))

Simplify

= - ln (x) cos (x) + Ci (x)

Add a constant to the solution

= - ln (x) cos (x) + Ci (x) + C

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