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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Apply Integration By Parts

= - 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

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