1
/
|
| x / 5 / 3\\ / 5 / 3\\
| ------ dx = - RootSum\1 + 1071875*t , t -> t*log\-6125*t // + RootSum\1 + 1071875*t , t -> t*log\1 - 6125*t //
| 5
| x + 7
|
/
0
$${{\sqrt{10-2\,\sqrt{5}}\,\arctan \left({{\sqrt{10-2\,\sqrt{5}}\,
\left(\left(2\,\sqrt{5}+10\right)\,7^{{{4}\over{5}}}-21\,\sqrt{5}-35
\right)}\over{140}}\right)}\over{20\,7^{{{3}\over{5}}}}}+{{\sqrt{10-
2\,\sqrt{5}}\,\arctan \left({{\sqrt{10-2\,\sqrt{5}}\,\left(\left(2\,
\sqrt{5}+10\right)\,7^{{{4}\over{5}}}-21\,\sqrt{5}-35\right)}\over{
140}}\right)}\over{4\,\sqrt{5}\,7^{{{3}\over{5}}}}}+{{\sqrt{2\,
\sqrt{5}+10}\,\arctan \left({{\sqrt{2\,\sqrt{5}+10}\,\left(\left(2\,
\sqrt{5}-10\right)\,7^{{{4}\over{5}}}-21\,\sqrt{5}+35\right)}\over{
140}}\right)}\over{4\,\sqrt{5}\,7^{{{3}\over{5}}}}}-{{\sqrt{2\,
\sqrt{5}+10}\,\arctan \left({{\sqrt{2\,\sqrt{5}+10}\,\left(\left(2\,
\sqrt{5}-10\right)\,7^{{{4}\over{5}}}-21\,\sqrt{5}+35\right)}\over{
140}}\right)}\over{20\,7^{{{3}\over{5}}}}}+{{\log \left(2\,7^{{{2
}\over{5}}}+\left(\sqrt{5}-1\right)\,7^{{{1}\over{5}}}+2\right)
}\over{4\,\sqrt{5}\,7^{{{3}\over{5}}}}}+{{\log \left(2\,7^{{{2
}\over{5}}}+\left(\sqrt{5}-1\right)\,7^{{{1}\over{5}}}+2\right)
}\over{20\,7^{{{3}\over{5}}}}}-{{\log \left(2\,7^{{{2}\over{5}}}+
\left(-\sqrt{5}-1\right)\,7^{{{1}\over{5}}}+2\right)}\over{4\,\sqrt{
5}\,7^{{{3}\over{5}}}}}+{{\log \left(2\,7^{{{2}\over{5}}}+\left(-
\sqrt{5}-1\right)\,7^{{{1}\over{5}}}+2\right)}\over{20\,7^{{{3
}\over{5}}}}}-{{\log \left(2\,7^{{{2}\over{5}}}\right)}\over{10\,7^{
{{3}\over{5}}}}}-{{\log \left(7^{{{1}\over{5}}}+1\right)}\over{5\,7
^{{{3}\over{5}}}}}+{{\sqrt{10-2\,\sqrt{5}}\,\arctan \left({{\sqrt{10
-2\,\sqrt{5}}\,\left(3\,\sqrt{5}+5\right)}\over{20}}\right)}\over{4
\,\sqrt{5}\,7^{{{3}\over{5}}}}}+{{\sqrt{10-2\,\sqrt{5}}\,\arctan
\left({{\sqrt{10-2\,\sqrt{5}}\,\left(3\,\sqrt{5}+5\right)}\over{20}}
\right)}\over{20\,7^{{{3}\over{5}}}}}+{{\sqrt{2\,\sqrt{5}+10}\,
\arctan \left({{\sqrt{2\,\sqrt{5}+10}\,\left(3\,\sqrt{5}-5\right)
}\over{20}}\right)}\over{4\,\sqrt{5}\,7^{{{3}\over{5}}}}}-{{\sqrt{2
\,\sqrt{5}+10}\,\arctan \left({{\sqrt{2\,\sqrt{5}+10}\,\left(3\,
\sqrt{5}-5\right)}\over{20}}\right)}\over{20\,7^{{{3}\over{5}}}}}+{{
\log 7}\over{25\,7^{{{3}\over{5}}}}}$$
Ответ (Неопределённый)
[src] /
|
| x / 5 / 3\\
| ------ dx = C + RootSum\1 + 1071875*t , t -> t*log\x - 6125*t //
| 5
| x + 7
|
/
$$-{{\log \left(2\,x^2+\left(\sqrt{5}-1\right)\,7^{{{1}\over{5}}}\,x+
2\,7^{{{2}\over{5}}}\right)}\over{\left(5-5^{{{3}\over{2}}}\right)\,
7^{{{3}\over{5}}}}}-{{\log \left(2\,x^2+\left(-\sqrt{5}-1\right)\,7
^{{{1}\over{5}}}\,x+2\,7^{{{2}\over{5}}}\right)}\over{\left(5^{{{3
}\over{2}}}+5\right)\,7^{{{3}\over{5}}}}}-{{2\,\arctan \left({{4\,x+
\left(\sqrt{5}-1\right)\,7^{{{1}\over{5}}}}\over{\sqrt{2\,\sqrt{5}+
10}\,7^{{{1}\over{5}}}}}\right)}\over{\sqrt{5}\,\sqrt{2\,\sqrt{5}+10
}\,7^{{{3}\over{5}}}}}+{{2\,\arctan \left({{4\,x+\left(-\sqrt{5}-1
\right)\,7^{{{1}\over{5}}}}\over{\sqrt{10-2\,\sqrt{5}}\,7^{{{1
}\over{5}}}}}\right)}\over{\sqrt{5}\,\sqrt{10-2\,\sqrt{5}}\,7^{{{3
}\over{5}}}}}-{{\log \left(x+7^{{{1}\over{5}}}\right)}\over{5\,7^{{{
3}\over{5}}}}}$$
