Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I've been told to evaluate the indefinite integral of this function:

$$\int \sin {\ln {x}} dx$$

I'm supposed to make a $u$-substitution in the beginning, then complete it using integration by parts. Every time I try, I just end up going in circles. Could someone please help me? Thanks!

share|cite|improve this question

Hint: Let $u = \ln{x}$. Then $du = \frac{1}{x} dx$, or $x du = dx$. Using the fact that $x = e^u$, we can write

$$\int \sin \ln{x} dx = \int e^u \sin{u}du$$

This is a common integral that can be done by using parts twice, or by recognizing that

$$\sin{u} = \operatorname{Im} e^{iu}$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.