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

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

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

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

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

Solution steps

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

Apply Integration By Parts

: ln (sin (x)) sin (x) - \int cos (x) d x

= ln (sin (x)) sin (x) - \int cos (x) d x

\int cos (x) d x = sin (x)

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

Add a constant to the solution

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

\frac{d}{d t} (\frac{t}{t ^{2} + 1})

x \to 1 lim (x^{2} - 8 x - 1)

f (x) = \frac{e ^{x}}{3 + e ^{x}}

x \to 3 - lim (x^{2} - 9)

y = 3 (x + 1), y = 4 (x + 1), x = 6

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