Optimal. Leaf size=40 \[ \frac {25 \left (-x+x^2\right )}{-5+\frac {3}{\log \left (x-\frac {\left (e^4-x\right )^2}{\left (\frac {4}{x}+x\right )^2}\right )}} \]
________________________________________________________________________________________
Rubi [F] time = 10.45, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {4800-4800 x+3600 x^2-4800 x^3+2100 x^4-900 x^5+75 x^6-75 x^7+e^8 \left (-600 x+600 x^2+150 x^3-150 x^4\right )+e^4 \left (1800 x^2-1800 x^3-150 x^4+150 x^5\right )+\left (4800-9600 x+3600 x^2-7500 x^3+1500 x^4-1875 x^5+225 x^6-150 x^7+e^8 \left (-300 x+600 x^2-75 x^3+150 x^4\right )+e^4 \left (600 x^2-1200 x^3+150 x^4-300 x^5\right )\right ) \log \left (\frac {16 x-e^8 x^2+8 x^3+2 e^4 x^3-x^4+x^5}{16+8 x^2+x^4}\right )+\left (-8000+16000 x-6000 x^2+12500 x^3-2500 x^4+3125 x^5-375 x^6+250 x^7+e^8 \left (500 x-1000 x^2+125 x^3-250 x^4\right )+e^4 \left (-1000 x^2+2000 x^3-250 x^4+500 x^5\right )\right ) \log ^2\left (\frac {16 x-e^8 x^2+8 x^3+2 e^4 x^3-x^4+x^5}{16+8 x^2+x^4}\right )}{-576-432 x^2+36 x^3-108 x^4+9 x^5-9 x^6+e^8 \left (36 x+9 x^3\right )+e^4 \left (-72 x^2-18 x^4\right )+\left (1920+1440 x^2-120 x^3+360 x^4-30 x^5+30 x^6+e^8 \left (-120 x-30 x^3\right )+e^4 \left (240 x^2+60 x^4\right )\right ) \log \left (\frac {16 x-e^8 x^2+8 x^3+2 e^4 x^3-x^4+x^5}{16+8 x^2+x^4}\right )+\left (-1600-1200 x^2+100 x^3-300 x^4+25 x^5-25 x^6+e^8 \left (100 x+25 x^3\right )+e^4 \left (-200 x^2-50 x^4\right )\right ) \log ^2\left (\frac {16 x-e^8 x^2+8 x^3+2 e^4 x^3-x^4+x^5}{16+8 x^2+x^4}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 \left (-192+192 x-144 x^2+192 x^3-84 x^4+36 x^5-3 x^6+3 x^7-6 e^4 x^2 \left (12-12 x-x^2+x^3\right )+6 e^8 x \left (4-4 x-x^2+x^3\right )+3 \left (-64+4 \left (32+e^8\right ) x-8 \left (6+e^4+e^8\right ) x^2+\left (100+16 e^4+e^8\right ) x^3-2 \left (10+e^4+e^8\right ) x^4+\left (25+4 e^4\right ) x^5-3 x^6+2 x^7\right ) \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )-5 \left (-64+4 \left (32+e^8\right ) x-8 \left (6+e^4+e^8\right ) x^2+\left (100+16 e^4+e^8\right ) x^3-2 \left (10+e^4+e^8\right ) x^4+\left (25+4 e^4\right ) x^5-3 x^6+2 x^7\right ) \log ^2\left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )}{\left (64+48 x^2-4 x^3+12 x^4-x^5+x^6-e^8 x \left (4+x^2\right )+2 e^4 x^2 \left (4+x^2\right )\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ &=25 \int \frac {-192+192 x-144 x^2+192 x^3-84 x^4+36 x^5-3 x^6+3 x^7-6 e^4 x^2 \left (12-12 x-x^2+x^3\right )+6 e^8 x \left (4-4 x-x^2+x^3\right )+3 \left (-64+4 \left (32+e^8\right ) x-8 \left (6+e^4+e^8\right ) x^2+\left (100+16 e^4+e^8\right ) x^3-2 \left (10+e^4+e^8\right ) x^4+\left (25+4 e^4\right ) x^5-3 x^6+2 x^7\right ) \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )-5 \left (-64+4 \left (32+e^8\right ) x-8 \left (6+e^4+e^8\right ) x^2+\left (100+16 e^4+e^8\right ) x^3-2 \left (10+e^4+e^8\right ) x^4+\left (25+4 e^4\right ) x^5-3 x^6+2 x^7\right ) \log ^2\left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )}{\left (64+48 x^2-4 x^3+12 x^4-x^5+x^6-e^8 x \left (4+x^2\right )+2 e^4 x^2 \left (4+x^2\right )\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ &=25 \int \left (\frac {1}{5} (1-2 x)+\frac {3 \left (-64+64 \left (1+\frac {e^8}{8}\right ) x-48 \left (1+\frac {1}{6} e^4 \left (3+e^4\right )\right ) x^2+64 \left (1-\frac {1}{32} e^4 \left (-12+e^4\right )\right ) x^3-28 \left (1-\frac {1}{14} e^4 \left (1+e^4\right )\right ) x^4+12 \left (1-\frac {e^4}{6}\right ) x^5-x^6+x^7\right )}{\left (4+x^2\right ) \left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}-\frac {3 (-1+2 x)}{5 \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )}\right ) \, dx\\ &=-\frac {5}{4} (1-2 x)^2-15 \int \frac {-1+2 x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx+75 \int \frac {-64+64 \left (1+\frac {e^8}{8}\right ) x-48 \left (1+\frac {1}{6} e^4 \left (3+e^4\right )\right ) x^2+64 \left (1-\frac {1}{32} e^4 \left (-12+e^4\right )\right ) x^3-28 \left (1-\frac {1}{14} e^4 \left (1+e^4\right )\right ) x^4+12 \left (1-\frac {e^4}{6}\right ) x^5-x^6+x^7}{\left (4+x^2\right ) \left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ &=-\frac {5}{4} (1-2 x)^2-15 \int \left (\frac {1}{3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )}+\frac {2 x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )}\right ) \, dx+75 \int \left (\frac {48-2 \left (32+e^8\right ) x+\left (8+2 e^4+3 e^8\right ) x^2-4 \left (4+e^4\right ) x^3}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {x}{\left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {16 (-1+x)}{\left (4+x^2\right ) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}\right ) \, dx\\ &=-\frac {5}{4} (1-2 x)^2-15 \int \frac {1}{3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx-30 \int \frac {x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx+75 \int \frac {48-2 \left (32+e^8\right ) x+\left (8+2 e^4+3 e^8\right ) x^2-4 \left (4+e^4\right ) x^3}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+75 \int \frac {x}{\left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+1200 \int \frac {-1+x}{\left (4+x^2\right ) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ &=-\frac {5}{4} (1-2 x)^2-15 \int \frac {1}{3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx-30 \int \frac {x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx+75 \int \left (\frac {48}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {2 \left (-32-e^8\right ) x}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {\left (8+2 e^4+3 e^8\right ) x^2}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {4 \left (-4-e^4\right ) x^3}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}\right ) \, dx+75 \int \frac {x}{\left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+1200 \int \left (-\frac {1}{\left (4+x^2\right ) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {x}{\left (4+x^2\right ) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}\right ) \, dx\\ &=-\frac {5}{4} (1-2 x)^2-15 \int \frac {1}{3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx-30 \int \frac {x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx+75 \int \frac {x}{\left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-1200 \int \frac {1}{\left (4+x^2\right ) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+1200 \int \frac {x}{\left (4+x^2\right ) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+3600 \int \frac {1}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-\left (300 \left (4+e^4\right )\right ) \int \frac {x^3}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-\left (150 \left (32+e^8\right )\right ) \int \frac {x}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+\left (75 \left (8+2 e^4+3 e^8\right )\right ) \int \frac {x^2}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ &=-\frac {5}{4} (1-2 x)^2-15 \int \frac {1}{3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx-30 \int \frac {x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx+75 \int \frac {x}{\left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-1200 \int \left (\frac {i}{4 (2 i-x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {i}{4 (2 i+x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}\right ) \, dx+1200 \int \left (-\frac {1}{2 (2 i-x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}+\frac {1}{2 (2 i+x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2}\right ) \, dx+3600 \int \frac {1}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-\left (300 \left (4+e^4\right )\right ) \int \frac {x^3}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-\left (150 \left (32+e^8\right )\right ) \int \frac {x}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+\left (75 \left (8+2 e^4+3 e^8\right )\right ) \int \frac {x^2}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ &=-\frac {5}{4} (1-2 x)^2-300 i \int \frac {1}{(2 i-x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-300 i \int \frac {1}{(2 i+x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-15 \int \frac {1}{3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx-30 \int \frac {x}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )} \, dx+75 \int \frac {x}{\left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-600 \int \frac {1}{(2 i-x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+600 \int \frac {1}{(2 i+x) \left (-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+3600 \int \frac {1}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-\left (300 \left (4+e^4\right )\right ) \int \frac {x^3}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx-\left (150 \left (32+e^8\right )\right ) \int \frac {x}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx+\left (75 \left (8+2 e^4+3 e^8\right )\right ) \int \frac {x^2}{\left (16-e^8 x+2 \left (4+e^4\right ) x^2-x^3+x^4\right ) \left (3-5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.33, size = 58, normalized size = 1.45 \begin {gather*} 5 x \left (1-x-\frac {3 (-1+x)}{-3+5 \log \left (\frac {x \left (16-e^8 x+8 x^2+2 e^4 x^2-x^3+x^4\right )}{\left (4+x^2\right )^2}\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.54, size = 105, normalized size = 2.62 \begin {gather*} -\frac {25 \, {\left (x^{2} - x\right )} \log \left (\frac {x^{5} - x^{4} + 2 \, x^{3} e^{4} + 8 \, x^{3} - x^{2} e^{8} + 16 \, x}{x^{4} + 8 \, x^{2} + 16}\right )}{5 \, \log \left (\frac {x^{5} - x^{4} + 2 \, x^{3} e^{4} + 8 \, x^{3} - x^{2} e^{8} + 16 \, x}{x^{4} + 8 \, x^{2} + 16}\right ) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 1.43, size = 67, normalized size = 1.68
method | result | size |
risch | \(-5 x^{2}+5 x -\frac {15 x \left (x -1\right )}{5 \ln \left (\frac {-x^{2} {\mathrm e}^{8}+2 x^{3} {\mathrm e}^{4}+x^{5}-x^{4}+8 x^{3}+16 x}{x^{4}+8 x^{2}+16}\right )-3}\) | \(67\) |
norman | \(\frac {25 x \ln \left (\frac {-x^{2} {\mathrm e}^{8}+2 x^{3} {\mathrm e}^{4}+x^{5}-x^{4}+8 x^{3}+16 x}{x^{4}+8 x^{2}+16}\right )-25 x^{2} \ln \left (\frac {-x^{2} {\mathrm e}^{8}+2 x^{3} {\mathrm e}^{4}+x^{5}-x^{4}+8 x^{3}+16 x}{x^{4}+8 x^{2}+16}\right )}{5 \ln \left (\frac {-x^{2} {\mathrm e}^{8}+2 x^{3} {\mathrm e}^{4}+x^{5}-x^{4}+8 x^{3}+16 x}{x^{4}+8 x^{2}+16}\right )-3}\) | \(158\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.61, size = 104, normalized size = 2.60 \begin {gather*} -\frac {25 \, {\left ({\left (x^{2} - x\right )} \log \left (x^{4} - x^{3} + 2 \, x^{2} {\left (e^{4} + 4\right )} - x e^{8} + 16\right ) - 2 \, {\left (x^{2} - x\right )} \log \left (x^{2} + 4\right ) + {\left (x^{2} - x\right )} \log \relax (x)\right )}}{5 \, \log \left (x^{4} - x^{3} + 2 \, x^{2} {\left (e^{4} + 4\right )} - x e^{8} + 16\right ) - 10 \, \log \left (x^{2} + 4\right ) + 5 \, \log \relax (x) - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.15, size = 460, normalized size = 11.50 \begin {gather*} 14\,x+\frac {\left (24\,{\mathrm {e}}^4+18\,{\mathrm {e}}^8-144\right )\,x^5+\left (378\,{\mathrm {e}}^4-69\,{\mathrm {e}}^8+168\right )\,x^4+\left (48\,{\mathrm {e}}^{12}-18\,{\mathrm {e}}^8-576\,{\mathrm {e}}^4-336\right )\,x^3+\left (1224\,{\mathrm {e}}^4+636\,{\mathrm {e}}^8+144\right )\,x^2+\left (-24\,{\mathrm {e}}^8-192\,{\mathrm {e}}^{12}-384\right )\,x+1536\,{\mathrm {e}}^4+192}{x^6+\left (12-2\,{\mathrm {e}}^4\right )\,x^4+\left (2\,{\mathrm {e}}^8-16\right )\,x^3+\left (24\,{\mathrm {e}}^4+48\right )\,x^2-8\,{\mathrm {e}}^8\,x+64}-\frac {\frac {3\,x\,\left (704\,x+52\,x\,{\mathrm {e}}^8-144\,x^2\,{\mathrm {e}}^4+168\,x^3\,{\mathrm {e}}^4+4\,x^4\,{\mathrm {e}}^4+2\,x^5\,{\mathrm {e}}^4-64\,x^2\,{\mathrm {e}}^8-7\,x^3\,{\mathrm {e}}^8+4\,x^4\,{\mathrm {e}}^8-384\,x^2+620\,x^3-200\,x^4+135\,x^5-14\,x^6+11\,x^7-512\right )}{24\,x^2\,{\mathrm {e}}^4-8\,x\,{\mathrm {e}}^8-2\,x^4\,{\mathrm {e}}^4+2\,x^3\,{\mathrm {e}}^8+48\,x^2-16\,x^3+12\,x^4+x^6+64}-\frac {15\,x\,\ln \left (\frac {16\,x+2\,x^3\,{\mathrm {e}}^4-x^2\,{\mathrm {e}}^8+8\,x^3-x^4+x^5}{x^4+8\,x^2+16}\right )\,\left (2\,x-1\right )\,\left (x^2+4\right )\,\left (2\,x^2\,{\mathrm {e}}^4-x\,{\mathrm {e}}^8+8\,x^2-x^3+x^4+16\right )}{24\,x^2\,{\mathrm {e}}^4-8\,x\,{\mathrm {e}}^8-2\,x^4\,{\mathrm {e}}^4+2\,x^3\,{\mathrm {e}}^8+48\,x^2-16\,x^3+12\,x^4+x^6+64}}{5\,\ln \left (\frac {16\,x+2\,x^3\,{\mathrm {e}}^4-x^2\,{\mathrm {e}}^8+8\,x^3-x^4+x^5}{x^4+8\,x^2+16}\right )-3}-11\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 1.59, size = 61, normalized size = 1.52 \begin {gather*} - 5 x^{2} + 5 x + \frac {- 15 x^{2} + 15 x}{5 \log {\left (\frac {x^{5} - x^{4} + 8 x^{3} + 2 x^{3} e^{4} - x^{2} e^{8} + 16 x}{x^{4} + 8 x^{2} + 16} \right )} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________