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How to calculate this integral?

$$I=\int_{X_0}^{X}(\log t)\,(\tan^2t)\,\mathrm{d}t.$$

I tried integrate by parts and I found something related to:

$$J=\int_{X_0}^{X}\dfrac{\log\cos t}{t^2}\,\mathrm{d}t.$$

Jika
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    You have bounds $0$ and $\infty$ in the title but some other numbers in the body, which is it? – Jean-Sébastien May 02 '14 at 13:39
  • Because when I tried to do it by parts, I found some infinity problems like $[\log t \tan t]_{0}^{\infty}$. So I changed the values to $X_0$ and $X$ and I calculated the limits after that. But I would like to know the value of I in the title. Thanks – Jika May 02 '14 at 13:46
  • Do you mean $\int\log{\left(t\tan^2{t}\right)}dt$? – David H May 02 '14 at 13:51
  • @DavidH No, see the edit. – Jika May 02 '14 at 13:52
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    $\int_{0}^{+\infty} \big( \log(t) \big) \big( \tan^{2}(t) \big) dt$ does not converge... The function $t , \longmapsto , \log(t) \big( \tan^{2}(t) \big)$ is not integrable at $t=\frac{\pi}{2}$ (and at all $\frac{k\pi}{2}$, $k \in \mathbb{N})$. – pitchounet May 02 '14 at 14:24

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