Optimal. Leaf size=354 \[ -\frac {\left (2100 d^5+675 d^4 e+1110 d^3 e^2+222 d^2 e^3+444 d e^4-65 e^5\right ) x}{e^8}+\frac {\left (1500 d^4+450 d^3 e+666 d^2 e^2+111 d e^3+148 e^4\right ) x^2}{2 e^7}-\frac {\left (1000 d^3+270 d^2 e+333 d e^2+37 e^3\right ) x^3}{3 e^6}+\frac {3 \left (200 d^2+45 d e+37 e^2\right ) x^4}{4 e^5}-\frac {3 (20 d+3 e) x^5}{e^4}+\frac {50 x^6}{3 e^3}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right )}{2 e^9 (d+e x)^2}+\frac {\left (5 d^2-2 d e+3 e^2\right ) \left (160 d^5+127 d^4 e+88 d^3 e^2-4 d^2 e^3+64 d e^4-11 e^5\right )}{e^9 (d+e x)}+\frac {\left (2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6\right ) \log (d+e x)}{e^9} \]
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Rubi [A]
time = 0.22, antiderivative size = 354, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {1642}
\begin {gather*} \frac {3 x^4 \left (200 d^2+45 d e+37 e^2\right )}{4 e^5}-\frac {x^3 \left (1000 d^3+270 d^2 e+333 d e^2+37 e^3\right )}{3 e^6}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right )}{2 e^9 (d+e x)^2}+\frac {x^2 \left (1500 d^4+450 d^3 e+666 d^2 e^2+111 d e^3+148 e^4\right )}{2 e^7}+\frac {\left (5 d^2-2 d e+3 e^2\right ) \left (160 d^5+127 d^4 e+88 d^3 e^2-4 d^2 e^3+64 d e^4-11 e^5\right )}{e^9 (d+e x)}-\frac {x \left (2100 d^5+675 d^4 e+1110 d^3 e^2+222 d^2 e^3+444 d e^4-65 e^5\right )}{e^8}+\frac {\left (2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6\right ) \log (d+e x)}{e^9}-\frac {3 x^5 (20 d+3 e)}{e^4}+\frac {50 x^6}{3 e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1642
Rubi steps
\begin {align*} \int \frac {\left (3+2 x+5 x^2\right )^2 \left (2+x+3 x^2-5 x^3+4 x^4\right )}{(d+e x)^3} \, dx &=\int \left (\frac {-2100 d^5-675 d^4 e-1110 d^3 e^2-222 d^2 e^3-444 d e^4+65 e^5}{e^8}+\frac {\left (1500 d^4+450 d^3 e+666 d^2 e^2+111 d e^3+148 e^4\right ) x}{e^7}-\frac {\left (1000 d^3+270 d^2 e+333 d e^2+37 e^3\right ) x^2}{e^6}+\frac {3 \left (200 d^2+45 d e+37 e^2\right ) x^3}{e^5}-\frac {15 (20 d+3 e) x^4}{e^4}+\frac {100 x^5}{e^3}+\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right )}{e^8 (d+e x)^3}+\frac {-800 d^7-315 d^6 e-666 d^5 e^2-185 d^4 e^3-592 d^3 e^4+195 d^2 e^5-214 d e^6+33 e^7}{e^8 (d+e x)^2}+\frac {2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6}{e^8 (d+e x)}\right ) \, dx\\ &=-\frac {\left (2100 d^5+675 d^4 e+1110 d^3 e^2+222 d^2 e^3+444 d e^4-65 e^5\right ) x}{e^8}+\frac {\left (1500 d^4+450 d^3 e+666 d^2 e^2+111 d e^3+148 e^4\right ) x^2}{2 e^7}-\frac {\left (1000 d^3+270 d^2 e+333 d e^2+37 e^3\right ) x^3}{3 e^6}+\frac {3 \left (200 d^2+45 d e+37 e^2\right ) x^4}{4 e^5}-\frac {3 (20 d+3 e) x^5}{e^4}+\frac {50 x^6}{3 e^3}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right )}{2 e^9 (d+e x)^2}+\frac {\left (5 d^2-2 d e+3 e^2\right ) \left (160 d^5+127 d^4 e+88 d^3 e^2-4 d^2 e^3+64 d e^4-11 e^5\right )}{e^9 (d+e x)}+\frac {\left (2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6\right ) \log (d+e x)}{e^9}\\ \end {align*}
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Mathematica [A]
time = 0.07, size = 311, normalized size = 0.88 \begin {gather*} \frac {9000 d^8-390 d^7 e (-9+40 x)-18 d^6 e^2 \left (-407+240 x+2300 x^2\right )-2 d^5 e^3 \left (-999+2664 x+6750 x^2+5600 x^3\right )+4 d^4 e^4 \left (1554-111 x-5661 x^2-945 x^3+700 x^4\right )-d^3 e^5 \left (1950-1776 x+4662 x^2+6660 x^3-945 x^4+1120 x^5\right )+d^2 e^6 \left (1926-1560 x-9768 x^2-1480 x^3+1665 x^4-378 x^5+560 x^6\right )+d e^7 \left (-198+2568 x+1560 x^2-3552 x^3+370 x^4-666 x^5+189 x^6-320 x^7\right )+e^8 \left (-108-396 x+780 x^3+888 x^4-148 x^5+333 x^6-108 x^7+200 x^8\right )+12 \left (2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6\right ) (d+e x)^2 \log (d+e x)}{12 e^9 (d+e x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 391, normalized size = 1.10
method | result | size |
norman | \(\frac {\frac {\left (5600 d^{7}+1890 d^{6} e +3330 d^{5} e^{2}+740 d^{4} e^{3}+1776 d^{3} e^{4}-390 d^{2} e^{5}+214 d \,e^{6}-33 e^{7}\right ) x}{e^{8}}+\frac {50 x^{8}}{3 e}+\frac {8400 d^{8}+2835 d^{7} e +4995 d^{6} e^{2}+1110 d^{5} e^{3}+2664 d^{4} e^{4}-585 d^{3} e^{5}+321 d^{2} e^{6}-33 d \,e^{7}-18 e^{8}}{2 e^{9}}-\frac {\left (80 d +27 e \right ) x^{7}}{3 e^{2}}+\frac {\left (560 d^{2}+189 d e +333 e^{2}\right ) x^{6}}{12 e^{3}}-\frac {\left (560 d^{3}+189 d^{2} e +333 d \,e^{2}+74 e^{3}\right ) x^{5}}{6 e^{4}}+\frac {\left (2800 d^{4}+945 d^{3} e +1665 d^{2} e^{2}+370 d \,e^{3}+888 e^{4}\right ) x^{4}}{12 e^{5}}-\frac {\left (2800 d^{5}+945 d^{4} e +1665 d^{3} e^{2}+370 d^{2} e^{3}+888 d \,e^{4}-195 e^{5}\right ) x^{3}}{3 e^{6}}}{\left (e x +d \right )^{2}}+\frac {\left (2800 d^{6}+945 d^{5} e +1665 d^{4} e^{2}+370 d^{3} e^{3}+888 d^{2} e^{4}-195 d \,e^{5}+107 e^{6}\right ) \ln \left (e x +d \right )}{e^{9}}\) | \(359\) |
default | \(\frac {\left (2800 d^{6}+945 d^{5} e +1665 d^{4} e^{2}+370 d^{3} e^{3}+888 d^{2} e^{4}-195 d \,e^{5}+107 e^{6}\right ) \ln \left (e x +d \right )}{e^{9}}-\frac {100 d^{8}+45 d^{7} e +111 d^{6} e^{2}+37 d^{5} e^{3}+148 d^{4} e^{4}-65 d^{3} e^{5}+107 d^{2} e^{6}-33 d \,e^{7}+18 e^{8}}{2 e^{9} \left (e x +d \right )^{2}}-\frac {-800 d^{7}-315 d^{6} e -666 d^{5} e^{2}-185 d^{4} e^{3}-592 d^{3} e^{4}+195 d^{2} e^{5}-214 d \,e^{6}+33 e^{7}}{e^{9} \left (e x +d \right )}-\frac {-\frac {50}{3} x^{6} e^{5}+60 x^{5} e^{4} d +9 x^{5} e^{5}-150 d^{2} e^{3} x^{4}-\frac {135}{4} x^{4} e^{4} d -\frac {111}{4} x^{4} e^{5}+\frac {1000}{3} d^{3} e^{2} x^{3}+90 d^{2} e^{3} x^{3}+111 d \,e^{4} x^{3}+\frac {37}{3} e^{5} x^{3}-750 d^{4} e \,x^{2}-225 d^{3} e^{2} x^{2}-333 d^{2} e^{3} x^{2}-\frac {111}{2} d \,e^{4} x^{2}-74 e^{5} x^{2}+2100 d^{5} x +675 d^{4} e x +1110 d^{3} e^{2} x +222 d^{2} e^{3} x +444 d \,e^{4} x -65 e^{5} x}{e^{8}}\) | \(391\) |
risch | \(\frac {107 \ln \left (e x +d \right )}{e^{3}}+\frac {74 x^{2}}{e^{3}}+\frac {65 x}{e^{3}}-\frac {9 x^{5}}{e^{3}}-\frac {37 x^{3}}{3 e^{3}}+\frac {50 x^{6}}{3 e^{3}}+\frac {\left (800 d^{7}+315 d^{6} e +666 d^{5} e^{2}+185 d^{4} e^{3}+592 d^{3} e^{4}-195 d^{2} e^{5}+214 d \,e^{6}-33 e^{7}\right ) x +\frac {1500 d^{8}+585 d^{7} e +1221 d^{6} e^{2}+333 d^{5} e^{3}+1036 d^{4} e^{4}-325 d^{3} e^{5}+321 d^{2} e^{6}-33 d \,e^{7}-18 e^{8}}{2 e}}{e^{8} \left (e x +d \right )^{2}}+\frac {1665 \ln \left (e x +d \right ) d^{4}}{e^{7}}+\frac {370 \ln \left (e x +d \right ) d^{3}}{e^{6}}+\frac {888 \ln \left (e x +d \right ) d^{2}}{e^{5}}-\frac {195 \ln \left (e x +d \right ) d}{e^{4}}+\frac {111 d \,x^{2}}{2 e^{4}}-\frac {1110 d^{3} x}{e^{6}}-\frac {222 d^{2} x}{e^{5}}-\frac {444 d x}{e^{4}}-\frac {111 d \,x^{3}}{e^{4}}+\frac {333 d^{2} x^{2}}{e^{5}}-\frac {90 d^{2} x^{3}}{e^{5}}+\frac {750 d^{4} x^{2}}{e^{7}}+\frac {225 d^{3} x^{2}}{e^{6}}-\frac {2100 d^{5} x}{e^{8}}-\frac {675 d^{4} x}{e^{7}}+\frac {2800 \ln \left (e x +d \right ) d^{6}}{e^{9}}+\frac {945 \ln \left (e x +d \right ) d^{5}}{e^{8}}-\frac {60 x^{5} d}{e^{4}}+\frac {150 d^{2} x^{4}}{e^{5}}+\frac {135 x^{4} d}{4 e^{4}}-\frac {1000 d^{3} x^{3}}{3 e^{6}}+\frac {111 x^{4}}{4 e^{3}}\) | \(423\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 342, normalized size = 0.97 \begin {gather*} {\left (2800 \, d^{6} + 945 \, d^{5} e + 1665 \, d^{4} e^{2} + 370 \, d^{3} e^{3} + 888 \, d^{2} e^{4} - 195 \, d e^{5} + 107 \, e^{6}\right )} e^{\left (-9\right )} \log \left (x e + d\right ) + \frac {1}{12} \, {\left (200 \, x^{6} e^{5} - 36 \, {\left (20 \, d e^{4} + 3 \, e^{5}\right )} x^{5} + 9 \, {\left (200 \, d^{2} e^{3} + 45 \, d e^{4} + 37 \, e^{5}\right )} x^{4} - 4 \, {\left (1000 \, d^{3} e^{2} + 270 \, d^{2} e^{3} + 333 \, d e^{4} + 37 \, e^{5}\right )} x^{3} + 6 \, {\left (1500 \, d^{4} e + 450 \, d^{3} e^{2} + 666 \, d^{2} e^{3} + 111 \, d e^{4} + 148 \, e^{5}\right )} x^{2} - 12 \, {\left (2100 \, d^{5} + 675 \, d^{4} e + 1110 \, d^{3} e^{2} + 222 \, d^{2} e^{3} + 444 \, d e^{4} - 65 \, e^{5}\right )} x\right )} e^{\left (-8\right )} + \frac {1500 \, d^{8} + 585 \, d^{7} e + 1221 \, d^{6} e^{2} + 333 \, d^{5} e^{3} + 1036 \, d^{4} e^{4} - 325 \, d^{3} e^{5} + 321 \, d^{2} e^{6} + 2 \, {\left (800 \, d^{7} e + 315 \, d^{6} e^{2} + 666 \, d^{5} e^{3} + 185 \, d^{4} e^{4} + 592 \, d^{3} e^{5} - 195 \, d^{2} e^{6} + 214 \, d e^{7} - 33 \, e^{8}\right )} x - 33 \, d e^{7} - 18 \, e^{8}}{2 \, {\left (x^{2} e^{11} + 2 \, d x e^{10} + d^{2} e^{9}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 501, normalized size = 1.42 \begin {gather*} \frac {9000 \, d^{8} + {\left (200 \, x^{8} - 108 \, x^{7} + 333 \, x^{6} - 148 \, x^{5} + 888 \, x^{4} + 780 \, x^{3} - 396 \, x - 108\right )} e^{8} - {\left (320 \, d x^{7} - 189 \, d x^{6} + 666 \, d x^{5} - 370 \, d x^{4} + 3552 \, d x^{3} - 1560 \, d x^{2} - 2568 \, d x + 198 \, d\right )} e^{7} + {\left (560 \, d^{2} x^{6} - 378 \, d^{2} x^{5} + 1665 \, d^{2} x^{4} - 1480 \, d^{2} x^{3} - 9768 \, d^{2} x^{2} - 1560 \, d^{2} x + 1926 \, d^{2}\right )} e^{6} - {\left (1120 \, d^{3} x^{5} - 945 \, d^{3} x^{4} + 6660 \, d^{3} x^{3} + 4662 \, d^{3} x^{2} - 1776 \, d^{3} x + 1950 \, d^{3}\right )} e^{5} + 4 \, {\left (700 \, d^{4} x^{4} - 945 \, d^{4} x^{3} - 5661 \, d^{4} x^{2} - 111 \, d^{4} x + 1554 \, d^{4}\right )} e^{4} - 2 \, {\left (5600 \, d^{5} x^{3} + 6750 \, d^{5} x^{2} + 2664 \, d^{5} x - 999 \, d^{5}\right )} e^{3} - 18 \, {\left (2300 \, d^{6} x^{2} + 240 \, d^{6} x - 407 \, d^{6}\right )} e^{2} - 390 \, {\left (40 \, d^{7} x - 9 \, d^{7}\right )} e + 12 \, {\left (2800 \, d^{8} + 107 \, x^{2} e^{8} - {\left (195 \, d x^{2} - 214 \, d x\right )} e^{7} + {\left (888 \, d^{2} x^{2} - 390 \, d^{2} x + 107 \, d^{2}\right )} e^{6} + {\left (370 \, d^{3} x^{2} + 1776 \, d^{3} x - 195 \, d^{3}\right )} e^{5} + 37 \, {\left (45 \, d^{4} x^{2} + 20 \, d^{4} x + 24 \, d^{4}\right )} e^{4} + 5 \, {\left (189 \, d^{5} x^{2} + 666 \, d^{5} x + 74 \, d^{5}\right )} e^{3} + 5 \, {\left (560 \, d^{6} x^{2} + 378 \, d^{6} x + 333 \, d^{6}\right )} e^{2} + 35 \, {\left (160 \, d^{7} x + 27 \, d^{7}\right )} e\right )} \log \left (x e + d\right )}{12 \, {\left (x^{2} e^{11} + 2 \, d x e^{10} + d^{2} e^{9}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.50, size = 394, normalized size = 1.11 \begin {gather*} x^{5} \left (- \frac {60 d}{e^{4}} - \frac {9}{e^{3}}\right ) + x^{4} \cdot \left (\frac {150 d^{2}}{e^{5}} + \frac {135 d}{4 e^{4}} + \frac {111}{4 e^{3}}\right ) + x^{3} \left (- \frac {1000 d^{3}}{3 e^{6}} - \frac {90 d^{2}}{e^{5}} - \frac {111 d}{e^{4}} - \frac {37}{3 e^{3}}\right ) + x^{2} \cdot \left (\frac {750 d^{4}}{e^{7}} + \frac {225 d^{3}}{e^{6}} + \frac {333 d^{2}}{e^{5}} + \frac {111 d}{2 e^{4}} + \frac {74}{e^{3}}\right ) + x \left (- \frac {2100 d^{5}}{e^{8}} - \frac {675 d^{4}}{e^{7}} - \frac {1110 d^{3}}{e^{6}} - \frac {222 d^{2}}{e^{5}} - \frac {444 d}{e^{4}} + \frac {65}{e^{3}}\right ) + \frac {1500 d^{8} + 585 d^{7} e + 1221 d^{6} e^{2} + 333 d^{5} e^{3} + 1036 d^{4} e^{4} - 325 d^{3} e^{5} + 321 d^{2} e^{6} - 33 d e^{7} - 18 e^{8} + x \left (1600 d^{7} e + 630 d^{6} e^{2} + 1332 d^{5} e^{3} + 370 d^{4} e^{4} + 1184 d^{3} e^{5} - 390 d^{2} e^{6} + 428 d e^{7} - 66 e^{8}\right )}{2 d^{2} e^{9} + 4 d e^{10} x + 2 e^{11} x^{2}} + \frac {50 x^{6}}{3 e^{3}} + \frac {\left (2800 d^{6} + 945 d^{5} e + 1665 d^{4} e^{2} + 370 d^{3} e^{3} + 888 d^{2} e^{4} - 195 d e^{5} + 107 e^{6}\right ) \log {\left (d + e x \right )}}{e^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.82, size = 354, normalized size = 1.00 \begin {gather*} {\left (2800 \, d^{6} + 945 \, d^{5} e + 1665 \, d^{4} e^{2} + 370 \, d^{3} e^{3} + 888 \, d^{2} e^{4} - 195 \, d e^{5} + 107 \, e^{6}\right )} e^{\left (-9\right )} \log \left ({\left | x e + d \right |}\right ) + \frac {1}{12} \, {\left (200 \, x^{6} e^{15} - 720 \, d x^{5} e^{14} + 1800 \, d^{2} x^{4} e^{13} - 4000 \, d^{3} x^{3} e^{12} + 9000 \, d^{4} x^{2} e^{11} - 25200 \, d^{5} x e^{10} - 108 \, x^{5} e^{15} + 405 \, d x^{4} e^{14} - 1080 \, d^{2} x^{3} e^{13} + 2700 \, d^{3} x^{2} e^{12} - 8100 \, d^{4} x e^{11} + 333 \, x^{4} e^{15} - 1332 \, d x^{3} e^{14} + 3996 \, d^{2} x^{2} e^{13} - 13320 \, d^{3} x e^{12} - 148 \, x^{3} e^{15} + 666 \, d x^{2} e^{14} - 2664 \, d^{2} x e^{13} + 888 \, x^{2} e^{15} - 5328 \, d x e^{14} + 780 \, x e^{15}\right )} e^{\left (-18\right )} + \frac {{\left (1500 \, d^{8} + 585 \, d^{7} e + 1221 \, d^{6} e^{2} + 333 \, d^{5} e^{3} + 1036 \, d^{4} e^{4} - 325 \, d^{3} e^{5} + 321 \, d^{2} e^{6} + 2 \, {\left (800 \, d^{7} e + 315 \, d^{6} e^{2} + 666 \, d^{5} e^{3} + 185 \, d^{4} e^{4} + 592 \, d^{3} e^{5} - 195 \, d^{2} e^{6} + 214 \, d e^{7} - 33 \, e^{8}\right )} x - 33 \, d e^{7} - 18 \, e^{8}\right )} e^{\left (-9\right )}}{2 \, {\left (x e + d\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.13, size = 771, normalized size = 2.18 \begin {gather*} x^4\,\left (\frac {111}{4\,e^3}-\frac {75\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{4\,e}\right )-x^3\,\left (\frac {37}{3\,e^3}+\frac {100\,d^3}{3\,e^6}+\frac {d\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{e}-\frac {d^2\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e^2}\right )-x^5\,\left (\frac {60\,d}{e^4}+\frac {9}{e^3}\right )+x\,\left (\frac {65}{e^3}-\frac {3\,d\,\left (\frac {148}{e^3}+\frac {3\,d\,\left (\frac {37}{e^3}+\frac {100\,d^3}{e^6}+\frac {3\,d\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{e}-\frac {3\,d^2\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e^2}\right )}{e}-\frac {3\,d^2\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{e^2}+\frac {d^3\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e^3}\right )}{e}+\frac {3\,d^2\,\left (\frac {37}{e^3}+\frac {100\,d^3}{e^6}+\frac {3\,d\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{e}-\frac {3\,d^2\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e^2}\right )}{e^2}-\frac {d^3\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{e^3}\right )+\frac {x\,\left (800\,d^7+315\,d^6\,e+666\,d^5\,e^2+185\,d^4\,e^3+592\,d^3\,e^4-195\,d^2\,e^5+214\,d\,e^6-33\,e^7\right )+\frac {1500\,d^8+585\,d^7\,e+1221\,d^6\,e^2+333\,d^5\,e^3+1036\,d^4\,e^4-325\,d^3\,e^5+321\,d^2\,e^6-33\,d\,e^7-18\,e^8}{2\,e}}{d^2\,e^8+2\,d\,e^9\,x+e^{10}\,x^2}+\frac {50\,x^6}{3\,e^3}+x^2\,\left (\frac {74}{e^3}+\frac {3\,d\,\left (\frac {37}{e^3}+\frac {100\,d^3}{e^6}+\frac {3\,d\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{e}-\frac {3\,d^2\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e^2}\right )}{2\,e}-\frac {3\,d^2\,\left (\frac {111}{e^3}-\frac {300\,d^2}{e^5}+\frac {3\,d\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{e}\right )}{2\,e^2}+\frac {d^3\,\left (\frac {300\,d}{e^4}+\frac {45}{e^3}\right )}{2\,e^3}\right )+\frac {\ln \left (d+e\,x\right )\,\left (2800\,d^6+945\,d^5\,e+1665\,d^4\,e^2+370\,d^3\,e^3+888\,d^2\,e^4-195\,d\,e^5+107\,e^6\right )}{e^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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