Optimal. Leaf size=25 \[ \frac {-1+e^x}{-\frac {3}{e^{x/4}-2 x}+x} \]
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Rubi [F] time = 3.65, 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 {-24+4 e^{x/2}+e^{x/4} (3-16 x)+16 x^2+e^x \left (24+24 x-16 x^2+16 x^3+e^{x/2} (-4+4 x)+e^{x/4} \left (-15+16 x-16 x^2\right )\right )}{36+48 x^2+4 e^{x/2} x^2+16 x^4+e^{x/4} \left (-24 x-16 x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-24+4 e^{x/2}+e^{x/4} (3-16 x)+16 x^2+e^x \left (24+24 x-16 x^2+16 x^3+e^{x/2} (-4+4 x)+e^{x/4} \left (-15+16 x-16 x^2\right )\right )}{4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx\\ &=\frac {1}{4} \int \frac {-24+4 e^{x/2}+e^{x/4} (3-16 x)+16 x^2+e^x \left (24+24 x-16 x^2+16 x^3+e^{x/2} (-4+4 x)+e^{x/4} \left (-15+16 x-16 x^2\right )\right )}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx\\ &=\frac {1}{4} \int \left (\frac {4 e^x (-1+x)}{x^2}+\frac {3 e^{3 x/4} (-8+3 x)}{x^3}+\frac {6 e^{x/2} \left (-18+3 x-4 x^2+2 x^3\right )}{x^4}+\frac {3 e^{x/4} \left (-144+9 x-96 x^2+12 x^3+4 x^5\right )}{x^5}+\frac {4 \left (-405-486 x^2-107 x^4+24 x^6\right )}{x^6}+\frac {3 \left (1944+81 x+3456 x^2+216 x^3+1720 x^4+215 x^5+96 x^7-128 x^8+16 x^9\right )}{x^6 \left (3-e^{x/4} x+2 x^2\right )}-\frac {3 \left (972+243 x+1944 x^2+810 x^3+852 x^4+1077 x^5-568 x^6+718 x^7-576 x^8+240 x^9-128 x^{10}+32 x^{11}\right )}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2}\right ) \, dx\\ &=\frac {3}{4} \int \frac {e^{3 x/4} (-8+3 x)}{x^3} \, dx+\frac {3}{4} \int \frac {e^{x/4} \left (-144+9 x-96 x^2+12 x^3+4 x^5\right )}{x^5} \, dx+\frac {3}{4} \int \frac {1944+81 x+3456 x^2+216 x^3+1720 x^4+215 x^5+96 x^7-128 x^8+16 x^9}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx-\frac {3}{4} \int \frac {972+243 x+1944 x^2+810 x^3+852 x^4+1077 x^5-568 x^6+718 x^7-576 x^8+240 x^9-128 x^{10}+32 x^{11}}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+\frac {3}{2} \int \frac {e^{x/2} \left (-18+3 x-4 x^2+2 x^3\right )}{x^4} \, dx+\int \frac {e^x (-1+x)}{x^2} \, dx+\int \frac {-405-486 x^2-107 x^4+24 x^6}{x^6} \, dx\\ &=\frac {3 e^{3 x/4}}{x^2}+\frac {e^x}{x}+\frac {3}{4} \int \left (4 e^{x/4}-\frac {144 e^{x/4}}{x^5}+\frac {9 e^{x/4}}{x^4}-\frac {96 e^{x/4}}{x^3}+\frac {12 e^{x/4}}{x^2}\right ) \, dx-\frac {3}{4} \int \left (-\frac {568}{\left (-3+e^{x/4} x-2 x^2\right )^2}+\frac {972}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2}+\frac {243}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2}+\frac {1944}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2}+\frac {810}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2}+\frac {852}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2}+\frac {1077}{x \left (3-e^{x/4} x+2 x^2\right )^2}+\frac {718 x}{\left (3-e^{x/4} x+2 x^2\right )^2}-\frac {576 x^2}{\left (3-e^{x/4} x+2 x^2\right )^2}+\frac {240 x^3}{\left (3-e^{x/4} x+2 x^2\right )^2}-\frac {128 x^4}{\left (3-e^{x/4} x+2 x^2\right )^2}+\frac {32 x^5}{\left (3-e^{x/4} x+2 x^2\right )^2}\right ) \, dx+\frac {3}{4} \int \left (\frac {1944}{x^6 \left (3-e^{x/4} x+2 x^2\right )}+\frac {81}{x^5 \left (3-e^{x/4} x+2 x^2\right )}+\frac {3456}{x^4 \left (3-e^{x/4} x+2 x^2\right )}+\frac {216}{x^3 \left (3-e^{x/4} x+2 x^2\right )}+\frac {1720}{x^2 \left (3-e^{x/4} x+2 x^2\right )}+\frac {215}{x \left (3-e^{x/4} x+2 x^2\right )}+\frac {96 x}{3-e^{x/4} x+2 x^2}-\frac {128 x^2}{3-e^{x/4} x+2 x^2}+\frac {16 x^3}{3-e^{x/4} x+2 x^2}\right ) \, dx+\frac {3}{2} \int \left (-\frac {18 e^{x/2}}{x^4}+\frac {3 e^{x/2}}{x^3}-\frac {4 e^{x/2}}{x^2}+\frac {2 e^{x/2}}{x}\right ) \, dx+\int \left (24-\frac {405}{x^6}-\frac {486}{x^4}-\frac {107}{x^2}\right ) \, dx\\ &=\frac {81}{x^5}+\frac {162}{x^3}+\frac {3 e^{3 x/4}}{x^2}+\frac {107}{x}+\frac {e^x}{x}+24 x+3 \int e^{x/4} \, dx+3 \int \frac {e^{x/2}}{x} \, dx+\frac {9}{2} \int \frac {e^{x/2}}{x^3} \, dx-6 \int \frac {e^{x/2}}{x^2} \, dx+\frac {27}{4} \int \frac {e^{x/4}}{x^4} \, dx+9 \int \frac {e^{x/4}}{x^2} \, dx+12 \int \frac {x^3}{3-e^{x/4} x+2 x^2} \, dx-24 \int \frac {x^5}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-27 \int \frac {e^{x/2}}{x^4} \, dx+\frac {243}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )} \, dx-72 \int \frac {e^{x/4}}{x^3} \, dx+72 \int \frac {x}{3-e^{x/4} x+2 x^2} \, dx+96 \int \frac {x^4}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-96 \int \frac {x^2}{3-e^{x/4} x+2 x^2} \, dx-108 \int \frac {e^{x/4}}{x^5} \, dx+\frac {645}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )} \, dx+162 \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )} \, dx-180 \int \frac {x^3}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {729}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+426 \int \frac {1}{\left (-3+e^{x/4} x-2 x^2\right )^2} \, dx+432 \int \frac {x^2}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1077}{2} \int \frac {x}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1215}{2} \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-639 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-729 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {3231}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1290 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )} \, dx-1458 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1458 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx+2592 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )} \, dx\\ &=12 e^{x/4}+\frac {81}{x^5}+\frac {27 e^{x/4}}{x^4}+\frac {162}{x^3}-\frac {9 e^{x/4}}{4 x^3}+\frac {9 e^{x/2}}{x^3}+\frac {36 e^{x/4}}{x^2}-\frac {9 e^{x/2}}{4 x^2}+\frac {3 e^{3 x/4}}{x^2}+\frac {107}{x}-\frac {9 e^{x/4}}{x}+\frac {6 e^{x/2}}{x}+\frac {e^x}{x}+24 x+3 \text {Ei}\left (\frac {x}{2}\right )+\frac {9}{16} \int \frac {e^{x/4}}{x^3} \, dx+\frac {9}{8} \int \frac {e^{x/2}}{x^2} \, dx+\frac {9}{4} \int \frac {e^{x/4}}{x} \, dx-3 \int \frac {e^{x/2}}{x} \, dx-\frac {9}{2} \int \frac {e^{x/2}}{x^3} \, dx-\frac {27}{4} \int \frac {e^{x/4}}{x^4} \, dx-9 \int \frac {e^{x/4}}{x^2} \, dx+12 \int \frac {x^3}{3-e^{x/4} x+2 x^2} \, dx-24 \int \frac {x^5}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx+\frac {243}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )} \, dx+72 \int \frac {x}{3-e^{x/4} x+2 x^2} \, dx+96 \int \frac {x^4}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-96 \int \frac {x^2}{3-e^{x/4} x+2 x^2} \, dx+\frac {645}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )} \, dx+162 \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )} \, dx-180 \int \frac {x^3}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {729}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+426 \int \frac {1}{\left (-3+e^{x/4} x-2 x^2\right )^2} \, dx+432 \int \frac {x^2}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1077}{2} \int \frac {x}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1215}{2} \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-639 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-729 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {3231}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1290 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )} \, dx-1458 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1458 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx+2592 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )} \, dx\\ &=12 e^{x/4}+\frac {81}{x^5}+\frac {27 e^{x/4}}{x^4}+\frac {162}{x^3}+\frac {9 e^{x/2}}{x^3}+\frac {1143 e^{x/4}}{32 x^2}+\frac {3 e^{3 x/4}}{x^2}+\frac {107}{x}+\frac {39 e^{x/2}}{8 x}+\frac {e^x}{x}+24 x+\frac {9 \text {Ei}\left (\frac {x}{4}\right )}{4}+\frac {9}{128} \int \frac {e^{x/4}}{x^2} \, dx-\frac {9}{16} \int \frac {e^{x/4}}{x^3} \, dx+\frac {9}{16} \int \frac {e^{x/2}}{x} \, dx-\frac {9}{8} \int \frac {e^{x/2}}{x^2} \, dx-\frac {9}{4} \int \frac {e^{x/4}}{x} \, dx+12 \int \frac {x^3}{3-e^{x/4} x+2 x^2} \, dx-24 \int \frac {x^5}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx+\frac {243}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )} \, dx+72 \int \frac {x}{3-e^{x/4} x+2 x^2} \, dx+96 \int \frac {x^4}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-96 \int \frac {x^2}{3-e^{x/4} x+2 x^2} \, dx+\frac {645}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )} \, dx+162 \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )} \, dx-180 \int \frac {x^3}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {729}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+426 \int \frac {1}{\left (-3+e^{x/4} x-2 x^2\right )^2} \, dx+432 \int \frac {x^2}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1077}{2} \int \frac {x}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1215}{2} \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-639 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-729 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {3231}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1290 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )} \, dx-1458 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1458 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx+2592 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )} \, dx\\ &=12 e^{x/4}+\frac {81}{x^5}+\frac {27 e^{x/4}}{x^4}+\frac {162}{x^3}+\frac {9 e^{x/2}}{x^3}+\frac {36 e^{x/4}}{x^2}+\frac {3 e^{3 x/4}}{x^2}+\frac {107}{x}-\frac {9 e^{x/4}}{128 x}+\frac {6 e^{x/2}}{x}+\frac {e^x}{x}+24 x+\frac {9 \text {Ei}\left (\frac {x}{2}\right )}{16}+\frac {9}{512} \int \frac {e^{x/4}}{x} \, dx-\frac {9}{128} \int \frac {e^{x/4}}{x^2} \, dx-\frac {9}{16} \int \frac {e^{x/2}}{x} \, dx+12 \int \frac {x^3}{3-e^{x/4} x+2 x^2} \, dx-24 \int \frac {x^5}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx+\frac {243}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )} \, dx+72 \int \frac {x}{3-e^{x/4} x+2 x^2} \, dx+96 \int \frac {x^4}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-96 \int \frac {x^2}{3-e^{x/4} x+2 x^2} \, dx+\frac {645}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )} \, dx+162 \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )} \, dx-180 \int \frac {x^3}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {729}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+426 \int \frac {1}{\left (-3+e^{x/4} x-2 x^2\right )^2} \, dx+432 \int \frac {x^2}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1077}{2} \int \frac {x}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1215}{2} \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-639 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-729 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {3231}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1290 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )} \, dx-1458 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1458 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx+2592 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )} \, dx\\ &=12 e^{x/4}+\frac {81}{x^5}+\frac {27 e^{x/4}}{x^4}+\frac {162}{x^3}+\frac {9 e^{x/2}}{x^3}+\frac {36 e^{x/4}}{x^2}+\frac {3 e^{3 x/4}}{x^2}+\frac {107}{x}+\frac {6 e^{x/2}}{x}+\frac {e^x}{x}+24 x+\frac {9 \text {Ei}\left (\frac {x}{4}\right )}{512}-\frac {9}{512} \int \frac {e^{x/4}}{x} \, dx+12 \int \frac {x^3}{3-e^{x/4} x+2 x^2} \, dx-24 \int \frac {x^5}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx+\frac {243}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )} \, dx+72 \int \frac {x}{3-e^{x/4} x+2 x^2} \, dx+96 \int \frac {x^4}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-96 \int \frac {x^2}{3-e^{x/4} x+2 x^2} \, dx+\frac {645}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )} \, dx+162 \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )} \, dx-180 \int \frac {x^3}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {729}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+426 \int \frac {1}{\left (-3+e^{x/4} x-2 x^2\right )^2} \, dx+432 \int \frac {x^2}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1077}{2} \int \frac {x}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1215}{2} \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-639 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-729 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {3231}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1290 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )} \, dx-1458 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1458 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx+2592 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )} \, dx\\ &=12 e^{x/4}+\frac {81}{x^5}+\frac {27 e^{x/4}}{x^4}+\frac {162}{x^3}+\frac {9 e^{x/2}}{x^3}+\frac {36 e^{x/4}}{x^2}+\frac {3 e^{3 x/4}}{x^2}+\frac {107}{x}+\frac {6 e^{x/2}}{x}+\frac {e^x}{x}+24 x+12 \int \frac {x^3}{3-e^{x/4} x+2 x^2} \, dx-24 \int \frac {x^5}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx+\frac {243}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )} \, dx+72 \int \frac {x}{3-e^{x/4} x+2 x^2} \, dx+96 \int \frac {x^4}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-96 \int \frac {x^2}{3-e^{x/4} x+2 x^2} \, dx+\frac {645}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )} \, dx+162 \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )} \, dx-180 \int \frac {x^3}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {729}{4} \int \frac {1}{x^5 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+426 \int \frac {1}{\left (-3+e^{x/4} x-2 x^2\right )^2} \, dx+432 \int \frac {x^2}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1077}{2} \int \frac {x}{\left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {1215}{2} \int \frac {1}{x^3 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-639 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-729 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx-\frac {3231}{4} \int \frac {1}{x \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1290 \int \frac {1}{x^2 \left (3-e^{x/4} x+2 x^2\right )} \, dx-1458 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )^2} \, dx+1458 \int \frac {1}{x^6 \left (3-e^{x/4} x+2 x^2\right )} \, dx+2592 \int \frac {1}{x^4 \left (3-e^{x/4} x+2 x^2\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 35, normalized size = 1.40 \begin {gather*} \frac {\left (-1+e^x\right ) \left (e^{x/4}-2 x\right )}{-3+e^{x/4} x-2 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 36, normalized size = 1.44 \begin {gather*} \frac {2 \, x e^{x} - 2 \, x - e^{\left (\frac {5}{4} \, x\right )} + e^{\left (\frac {1}{4} \, x\right )}}{2 \, x^{2} - x e^{\left (\frac {1}{4} \, x\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 53, normalized size = 2.12 \begin {gather*} \frac {2 \, x^{4} e^{x} - 2 \, x^{4} - x^{3} e^{\left (\frac {5}{4} \, x\right )} + x^{3} e^{\left (\frac {1}{4} \, x\right )}}{2 \, x^{5} - x^{4} e^{\left (\frac {1}{4} \, x\right )} + 3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.09, size = 116, normalized size = 4.64
method | result | size |
risch | \(24 x +\frac {107 x^{4}+162 x^{2}+81}{x^{5}}+\frac {{\mathrm e}^{x}}{x}+\frac {3 \,{\mathrm e}^{\frac {3 x}{4}}}{x^{2}}+\frac {3 \left (2 x^{2}+3\right ) {\mathrm e}^{\frac {x}{2}}}{x^{3}}+\frac {3 \left (4 x^{4}+12 x^{2}+9\right ) {\mathrm e}^{\frac {x}{4}}}{x^{4}}-\frac {3 \left (16 x^{8}+96 x^{6}+215 x^{4}+216 x^{2}+81\right )}{x^{5} \left (2 x^{2}-x \,{\mathrm e}^{\frac {x}{4}}+3\right )}\) | \(116\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 36, normalized size = 1.44 \begin {gather*} \frac {2 \, x e^{x} - 2 \, x - e^{\left (\frac {5}{4} \, x\right )} + e^{\left (\frac {1}{4} \, x\right )}}{2 \, x^{2} - x e^{\left (\frac {1}{4} \, x\right )} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 163, normalized size = 6.52 \begin {gather*} 24\,x+\frac {107\,x^4+162\,x^2+81}{x^5}+\frac {{\mathrm {e}}^x}{x}+\frac {3\,{\mathrm {e}}^{\frac {3\,x}{4}}}{x^2}+\frac {{\mathrm {e}}^{x/2}\,\left (6\,x^2+9\right )}{x^3}+\frac {{\mathrm {e}}^{x/4}\,\left (12\,x^4+36\,x^2+27\right )}{x^4}-\frac {3\,\left (32\,x^{11}-128\,x^{10}+240\,x^9-576\,x^8+718\,x^7-568\,x^6+1077\,x^5+852\,x^4+810\,x^3+1944\,x^2+243\,x+972\right )}{x^5\,\left (2\,x^2-x\,{\mathrm {e}}^{x/4}+3\right )\,\left (2\,x^3-8\,x^2+3\,x+12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.34, size = 116, normalized size = 4.64 \begin {gather*} 24 x + \frac {48 x^{8} + 288 x^{6} + 645 x^{4} + 648 x^{2} + 243}{- 2 x^{7} + x^{6} e^{\frac {x}{4}} - 3 x^{5}} + \frac {107 x^{4} + 162 x^{2} + 81}{x^{5}} + \frac {x^{9} e^{x} + 3 x^{8} e^{\frac {3 x}{4}} + \left (6 x^{9} + 9 x^{7}\right ) e^{\frac {x}{2}} + \left (12 x^{10} + 36 x^{8} + 27 x^{6}\right ) e^{\frac {x}{4}}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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