I have a function that is $$f(x) = x^2 \sin^2\left(x^2\log\left(\frac{1}{x}\right)\right)$$

here log is in base 10.

How to start of it to get a simplified step?

I tried taking $\log(1/x)=t$ and also tried one more substituion after this but there I got stuck.

Please help me solve this problem.

  • $\begingroup$ From Wolfram Alpha, it looks like there is no elementary antiderivative. $\endgroup$ – Ian Apr 15 '16 at 19:16
  • $\begingroup$ In the majority of cases, integrals won't have an elementary anti-derivative. It's often obvious when the integral looks like a composition of many functions, transcendental, trigonometric or otherwise. Intuition often tells you this is the case but Wolfram Alpha is a good check. $\endgroup$ – ÍgjøgnumMeg Apr 15 '16 at 20:20

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