Question How to solve $\int_{1}^{e^{37}}\frac{\pi sin\left(\pi \ln(x)\right)}{x}\, dx$

My Approach I don't have any idea about it .Please give me some hints.

Edit I made this post just for a hint to approach.I successfully got it,now i can solve it .Thanks for posting comments and answer

  • $\begingroup$ @Cornman Thanks for edit $\endgroup$ Dec 3, 2017 at 9:20
  • 1
    $\begingroup$ Let $\pi\ln x=u$. $\endgroup$
    – Nosrati
    Dec 3, 2017 at 9:21

1 Answer 1



Make $\log(x)=t\implies x=e^t\implies dx=e^t\,dt$ and see what happens for the antiderivative.

  • $\begingroup$ Indeed it was very easy.it is only the outfit that made it to look difficult. $\endgroup$ Dec 4, 2017 at 4:59

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