Integrand size = 90, antiderivative size = 27 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=-\frac {100}{e^5 x}+2 x \log \left (x+\frac {-3+2 x}{4 x^2}\right ) \]
[Out]
Time = 3.80 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11, number of steps used = 23, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 1608, 6874, 2104, 814, 648, 632, 210, 642, 2603} \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=2 x \log \left (-\frac {-4 x^3-2 x+3}{4 x^2}\right )-\frac {100}{e^5 x} \]
[In]
[Out]
Rule 12
Rule 210
Rule 632
Rule 642
Rule 648
Rule 814
Rule 1608
Rule 2104
Rule 2603
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{-3 x^2+2 x^3+4 x^5} \, dx}{e^5} \\ & = \frac {\int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{x^2 \left (-3+2 x+4 x^3\right )} \, dx}{e^5} \\ & = \frac {\int \left (\frac {4 \left (75-50 x-3 e^5 x^2-100 \left (1-\frac {e^5}{100}\right ) x^3-2 e^5 x^5\right )}{x^2 \left (3-2 x-4 x^3\right )}+2 e^5 \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )\right ) \, dx}{e^5} \\ & = 2 \int \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right ) \, dx+\frac {4 \int \frac {75-50 x-3 e^5 x^2-100 \left (1-\frac {e^5}{100}\right ) x^3-2 e^5 x^5}{x^2 \left (3-2 x-4 x^3\right )} \, dx}{e^5} \\ & = 2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )-2 \int \frac {-6+2 x-4 x^3}{3-2 x-4 x^3} \, dx+\frac {4 \int \left (\frac {e^5}{2}+\frac {25}{x^2}-\frac {e^5 (-9+4 x)}{2 \left (-3+2 x+4 x^3\right )}\right ) \, dx}{e^5} \\ & = -\frac {100}{e^5 x}+2 x+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )-2 \int \frac {-9+4 x}{-3+2 x+4 x^3} \, dx-2 \int \left (1-\frac {9-4 x}{3-2 x-4 x^3}\right ) \, dx \\ & = -\frac {100}{e^5 x}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )+2 \int \frac {9-4 x}{3-2 x-4 x^3} \, dx-32 \int \frac {-9+4 x}{\left (\frac {2}{3} \left (\frac {2\ 3^{2/3}}{\sqrt [3]{27+\sqrt {753}}}-\sqrt [3]{3 \left (27+\sqrt {753}\right )}\right )+4 x\right ) \left (\frac {4}{9} \left (6+\frac {12 \sqrt [3]{3}}{\left (27+\sqrt {753}\right )^{2/3}}+\left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right )-\frac {8 \left (2 \sqrt [3]{\frac {3}{27+\sqrt {753}}}-\sqrt [3]{27+\sqrt {753}}\right ) x}{3^{2/3}}+16 x^2\right )} \, dx \\ & = -\frac {100}{e^5 x}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )+32 \int \frac {9-4 x}{\left (-\frac {2}{3} \left (\frac {2\ 3^{2/3}}{\sqrt [3]{27+\sqrt {753}}}-\sqrt [3]{3 \left (27+\sqrt {753}\right )}\right )-4 x\right ) \left (\frac {4}{9} \left (6+\frac {12 \sqrt [3]{3}}{\left (27+\sqrt {753}\right )^{2/3}}+\left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right )-\frac {8 \left (2 \sqrt [3]{\frac {3}{27+\sqrt {753}}}-\sqrt [3]{27+\sqrt {753}}\right ) x}{3^{2/3}}+16 x^2\right )} \, dx-32 \int \left (\frac {\left (27+\sqrt {753}\right )^{2/3} \left (-4 3^{2/3}-27 \sqrt [3]{27+\sqrt {753}}+2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}\right )}{8 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right ) \left (2\ 3^{2/3}-\sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+6 \sqrt [3]{27+\sqrt {753}} x\right )}+\frac {\left (27+\sqrt {753}\right )^{2/3} \left (-\left (\left (9\ 3^{2/3}-\sqrt [6]{3} \sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}\right )+2 \left (27+\sqrt {753}\right )^{2/3}+\sqrt [3]{3} \left (247+9 \sqrt {753}\right )+\sqrt [3]{27+\sqrt {753}} \left (4\ 3^{2/3}+27 \sqrt [3]{27+\sqrt {753}}-2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}\right ) x\right )}{4 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right ) \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2\right )}\right ) \, dx \\ & = -\frac {100}{e^5 x}+\frac {2 \sqrt [3]{27+\sqrt {753}} \left (4 \sqrt [3]{3}+9\ 3^{2/3} \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right ) \log \left (2\ 3^{2/3}-\sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+6 \sqrt [3]{27+\sqrt {753}} x\right )}{3^{2/3} \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right )}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )+32 \int \left (\frac {\left (27+\sqrt {753}\right )^{2/3} \left (-4 3^{2/3}-27 \sqrt [3]{27+\sqrt {753}}+2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}\right )}{8 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right ) \left (2\ 3^{2/3}-\sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+6 \sqrt [3]{27+\sqrt {753}} x\right )}+\frac {\left (27+\sqrt {753}\right )^{2/3} \left (-\left (\left (9\ 3^{2/3}-\sqrt [6]{3} \sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}\right )+2 \left (27+\sqrt {753}\right )^{2/3}+\sqrt [3]{3} \left (247+9 \sqrt {753}\right )+\sqrt [3]{27+\sqrt {753}} \left (4\ 3^{2/3}+27 \sqrt [3]{27+\sqrt {753}}-2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}\right ) x\right )}{4 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right ) \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2\right )}\right ) \, dx-\frac {\left (8 \left (27+\sqrt {753}\right )^{2/3}\right ) \int \frac {-\left (\left (9\ 3^{2/3}-\sqrt [6]{3} \sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}\right )+2 \left (27+\sqrt {753}\right )^{2/3}+\sqrt [3]{3} \left (247+9 \sqrt {753}\right )+\sqrt [3]{27+\sqrt {753}} \left (4\ 3^{2/3}+27 \sqrt [3]{27+\sqrt {753}}-2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}\right ) x}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2} \, dx}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}} \\ & = -\frac {100}{e^5 x}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )+\frac {\left (8 \left (27+\sqrt {753}\right )^{2/3}\right ) \int \frac {-\left (\left (9\ 3^{2/3}-\sqrt [6]{3} \sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}\right )+2 \left (27+\sqrt {753}\right )^{2/3}+\sqrt [3]{3} \left (247+9 \sqrt {753}\right )+\sqrt [3]{27+\sqrt {753}} \left (4\ 3^{2/3}+27 \sqrt [3]{27+\sqrt {753}}-2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}\right ) x}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2} \, dx}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}}-\frac {\left (\left (27+\sqrt {753}\right )^{2/3} \left (27+\frac {4\ 3^{2/3}}{\sqrt [3]{27+\sqrt {753}}}-2 \sqrt [3]{3 \left (27+\sqrt {753}\right )}\right )\right ) \int \frac {2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right )+24 \left (27+\sqrt {753}\right )^{2/3} x}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2} \, dx}{3 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right )}-\frac {\left (6 \sqrt [6]{3} \left (502 \sqrt {3}+54 \sqrt {251}+251 \sqrt [6]{3} \left (27+\sqrt {753}\right )^{2/3}+9 \sqrt {251} \left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right )\right ) \int \frac {1}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2} \, dx}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}} \\ & = -\frac {100}{e^5 x}-\frac {\left (27+\sqrt {753}\right )^{2/3} \left (27+\frac {4\ 3^{2/3}}{\sqrt [3]{27+\sqrt {753}}}-2 \sqrt [3]{3 \left (27+\sqrt {753}\right )}\right ) \log \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2\right )}{3 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right )}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )+\frac {\left (\left (27+\sqrt {753}\right )^{2/3} \left (27+\frac {4\ 3^{2/3}}{\sqrt [3]{27+\sqrt {753}}}-2 \sqrt [3]{3 \left (27+\sqrt {753}\right )}\right )\right ) \int \frac {2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right )+24 \left (27+\sqrt {753}\right )^{2/3} x}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2} \, dx}{3 \left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right )}+\frac {\left (6 \sqrt [6]{3} \left (502 \sqrt {3}+54 \sqrt {251}+251 \sqrt [6]{3} \left (27+\sqrt {753}\right )^{2/3}+9 \sqrt {251} \left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right )\right ) \int \frac {1}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}+2 \left (27+\sqrt {753}\right )^{2/3}+2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right ) x+12 \left (27+\sqrt {753}\right )^{2/3} x^2} \, dx}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}}+\frac {\left (12 \sqrt [6]{3} \left (502 \sqrt {3}+54 \sqrt {251}+251 \sqrt [6]{3} \left (27+\sqrt {753}\right )^{2/3}+9 \sqrt {251} \left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right )\right ) \text {Subst}\left (\int \frac {1}{-72 \left (247\ 3^{2/3}+27 \sqrt [6]{3} \sqrt {251}+2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+2 \left (27+\sqrt {753}\right )^{4/3}\right )-x^2} \, dx,x,2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right )+24 \left (27+\sqrt {753}\right )^{2/3} x\right )}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}} \\ & = -\frac {100}{e^5 x}-\frac {\sqrt {2} \sqrt [6]{3} \left (502 \sqrt {3}+54 \sqrt {251}+251 \sqrt [6]{3} \left (27+\sqrt {753}\right )^{2/3}+9 \sqrt {251} \left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right ) \tan ^{-1}\left (\frac {\sqrt [3]{3} \left (27+\sqrt {753}-2 \sqrt [3]{3 \left (27+\sqrt {753}\right )}\right )+12 \left (27+\sqrt {753}\right )^{2/3} x}{3 \sqrt {2 \left (247\ 3^{2/3}+27 \sqrt [6]{3} \sqrt {251}+2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+2 \left (27+\sqrt {753}\right )^{4/3}\right )}}\right )}{\left (4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}\right ) \sqrt {247\ 3^{2/3}+27 \sqrt [6]{3} \sqrt {251}+2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+2 \left (27+\sqrt {753}\right )^{4/3}}}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right )-\frac {\left (12 \sqrt [6]{3} \left (502 \sqrt {3}+54 \sqrt {251}+251 \sqrt [6]{3} \left (27+\sqrt {753}\right )^{2/3}+9 \sqrt {251} \left (3 \left (27+\sqrt {753}\right )\right )^{2/3}\right )\right ) \text {Subst}\left (\int \frac {1}{-72 \left (247\ 3^{2/3}+27 \sqrt [6]{3} \sqrt {251}+2 \sqrt [3]{3} \left (27+\sqrt {753}\right )^{2/3}+2 \left (27+\sqrt {753}\right )^{4/3}\right )-x^2} \, dx,x,2\ 3^{2/3} \left (9\ 3^{2/3}+\sqrt [6]{3} \sqrt {251}-2 \sqrt [3]{27+\sqrt {753}}\right )+24 \left (27+\sqrt {753}\right )^{2/3} x\right )}{4 \sqrt [3]{3}+\sqrt [6]{3} \left (9 \sqrt {3}+\sqrt {251}\right ) \sqrt [3]{27+\sqrt {753}}-2 \left (27+\sqrt {753}\right )^{2/3}} \\ & = -\frac {100}{e^5 x}+2 x \log \left (-\frac {3-2 x-4 x^3}{4 x^2}\right ) \\ \end{align*}
Time = 0.19 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=-\frac {100}{e^5 x}+2 x \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right ) \]
[In]
[Out]
Time = 0.28 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04
method | result | size |
risch | \(2 x \ln \left (\frac {4 x^{3}+2 x -3}{4 x^{2}}\right )-\frac {100 \,{\mathrm e}^{-5}}{x}\) | \(28\) |
norman | \(\frac {-100 \,{\mathrm e}^{-5}+2 x^{2} \ln \left (\frac {4 x^{3}+2 x -3}{4 x^{2}}\right )}{x}\) | \(33\) |
parallelrisch | \(\frac {{\mathrm e}^{-5} \left (8 \ln \left (\frac {4 x^{3}+2 x -3}{4 x^{2}}\right ) {\mathrm e}^{5} x^{2}-400-2400 x \right )}{4 x}\) | \(38\) |
parts | \(-\frac {100 \,{\mathrm e}^{-5}}{x}-\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (4 \textit {\_Z}^{3}+2 \textit {\_Z} -3\right )}{\sum }\frac {\left (4 \textit {\_R} -9\right ) \ln \left (x -\textit {\_R} \right )}{6 \textit {\_R}^{2}+1}\right )-4 x \ln \left (2\right )+2 x \ln \left (\frac {4 x^{3}+2 x -3}{x^{2}}\right )-\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (4 \textit {\_Z}^{3}+2 \textit {\_Z} -3\right )}{\sum }\frac {\left (-4 \textit {\_R} +9\right ) \ln \left (x -\textit {\_R} \right )}{6 \textit {\_R}^{2}+1}\right )\) | \(108\) |
default | \({\mathrm e}^{-5} \left (-4 x \,{\mathrm e}^{5} \ln \left (2\right )+2 \,{\mathrm e}^{5} \left (x \ln \left (\frac {4 x^{3}+2 x -3}{x^{2}}\right )-x -\frac {\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (4 \textit {\_Z}^{3}+2 \textit {\_Z} -3\right )}{\sum }\frac {\left (-4 \textit {\_R} +9\right ) \ln \left (x -\textit {\_R} \right )}{6 \textit {\_R}^{2}+1}\right )}{2}\right )+2 x \,{\mathrm e}^{5}-\frac {100}{x}-\left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (4 \textit {\_Z}^{3}+2 \textit {\_Z} -3\right )}{\sum }\frac {\left (4 \textit {\_R} -9\right ) \ln \left (x -\textit {\_R} \right )}{6 \textit {\_R}^{2}+1}\right ) {\mathrm e}^{5}\right )\) | \(125\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=\frac {2 \, {\left (x^{2} e^{5} \log \left (\frac {4 \, x^{3} + 2 \, x - 3}{4 \, x^{2}}\right ) - 50\right )} e^{\left (-5\right )}}{x} \]
[In]
[Out]
Time = 0.09 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=2 x \log {\left (\frac {x^{3} + \frac {x}{2} - \frac {3}{4}}{x^{2}} \right )} - \frac {100}{x e^{5}} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.67 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=-\frac {2 \, {\left (2 \, x^{2} e^{5} \log \left (2\right ) - x^{2} e^{5} \log \left (4 \, x^{3} + 2 \, x - 3\right ) + 2 \, x^{2} e^{5} \log \left (x\right ) + 50\right )} e^{\left (-5\right )}}{x} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.15 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=\frac {2 \, {\left (x^{2} e^{5} \log \left (\frac {4 \, x^{3} + 2 \, x - 3}{4 \, x^{2}}\right ) - 50\right )} e^{\left (-5\right )}}{x} \]
[In]
[Out]
Time = 11.64 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {-300+200 x+400 x^3+e^5 \left (12 x^2-4 x^3+8 x^5\right )+e^5 \left (-6 x^2+4 x^3+8 x^5\right ) \log \left (\frac {-3+2 x+4 x^3}{4 x^2}\right )}{e^5 \left (-3 x^2+2 x^3+4 x^5\right )} \, dx=2\,x\,\ln \left (\frac {x^3+\frac {x}{2}-\frac {3}{4}}{x^2}\right )-\frac {100\,{\mathrm {e}}^{-5}}{x} \]
[In]
[Out]