The answer (Indefinite)
[src]
/ /
| |
| / 2 \ | / 2 \
| sin\log (x)/ | sin\log (x)/
| ------------ dx = C + | ------------ dx
| x | x
| |
/ /
$$\int \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx = C + \int \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx$$
1
/
|
| / 2 \
| sin\log (x)/
| ------------ dx
| x
|
/
0
$$-\lim_{x\downarrow 0}{{{\sqrt{\pi}\,\left(\sqrt{2}\,i+\sqrt{2}
\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\log x}\over{2}}\right)}\over{16}}+{{\sqrt{\pi}\,\left(\sqrt{2}\,i-
\sqrt{2}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i-\sqrt{2}
\right)\,\log x}\over{2}}\right)}\over{16}}+{{\sqrt{\pi}\,\left(
\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}\left(\sqrt{-i}\,\log x
\right)}\over{16}}+{{\sqrt{\pi}\,\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,\log x\right)
}\over{16}}}$$
=
1
/
|
| / 2 \
| sin\log (x)/
| ------------ dx
| x
|
/
0
$$\int\limits_{0}^{1} \frac{\sin{\left(\log{\left(x \right)}^{2} \right)}}{x}\, dx$$