Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm supposed do find some integrals. I am stuck with two of them.

The first one: $\displaystyle\int \operatorname{arcsin}\left(\frac{1}{x}\right) dx$

I have already integrated by parts having:

$$\displaystyle x \operatorname{arcsin}\left(\frac{1}{x}\right) + \int \frac{1}{\sqrt{1-x^2} \cdot x} dx$$

I tried further integration with substitution $\sqrt{1-x^2} = t$, but i wasn't able to get any result of it.

It would be nice if anyone could help my with the further integral.

Best regards!

share|improve this question
1  
I think you should recheck your work on integrating by parts, it doesn't look correct to me. Please note that $(\arcsin x)' = \frac{1}{\sqrt{1-x^2}}$. –  user49685 Mar 9 at 18:55

2 Answers 2

up vote 0 down vote accepted

As both user49685 and Claude Leibovici have pointed out, check the derivative of $\arcsin(\frac{1}{x})$.

Once you have fixed the error, for the resulting integral try the change of variable $x=\sec\theta$, noting that $\tan^2\theta=\sec^2\theta-1$.

share|improve this answer

Hint

As user49685 told, the derivative of $arcsin(1/x)$ is not what you wrote. Fix it and consider a change of variable such as $x=cosh(y)$.

share|improve this answer

Your Answer

 
discard

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.