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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{ln ( ( 4 x ) ^{3} )}{x} d x

\int x + x^{6} + x^{- 6} d x

\int \frac{x ^{2}}{5 - x ^{3}} d x

\int (cos^{2} (x)) sin (x) d x

\int \frac{cos ( x )}{9 + sin ^{2} ( x )} d x

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