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

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

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

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

Solution steps

\int ln (sin (x)) cos (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 x^{3} 1 + 49 x^{2} d x

\int (- 10 + \frac{7}{x}) d x

\int ln (x + y) d x

\int \frac{x ^{2} + 1}{x ^{3} + 10 x ^{2} + 21 x} d x

\int \frac{11 + x}{x} d x

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