Optimal. Leaf size=360 \[ \frac {2 \left (1750 d^4+450 d^3 e+555 d^2 e^2+74 d e^3+74 e^4\right ) x}{e^8}-\frac {\left (2000 d^3+450 d^2 e+444 d e^2+37 e^3\right ) x^2}{2 e^7}+\frac {\left (1000 d^2+180 d e+111 e^2\right ) x^3}{3 e^6}-\frac {5 (80 d+9 e) x^4}{4 e^5}+\frac {20 x^5}{e^4}-\frac {\left (5 d^2-2 d e+3 e^2\right )^2 \left (4 d^4+5 d^3 e+3 d^2 e^2-d e^3+2 e^4\right )}{3 e^9 (d+e x)^3}+\frac {\left (5 d^2-2 d e+3 e^2\right ) \left (160 d^5+127 d^4 e+88 d^3 e^2-4 d^2 e^3+64 d e^4-11 e^5\right )}{2 e^9 (d+e x)^2}-\frac {2800 d^6+945 d^5 e+1665 d^4 e^2+370 d^3 e^3+888 d^2 e^4-195 d e^5+107 e^6}{e^9 (d+e x)}-\frac {\left (5600 d^5+1575 d^4 e+2220 d^3 e^2+370 d^2 e^3+592 d e^4-65 e^5\right ) \log (d+e x)}{e^9} \]
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Rubi [A]
time = 0.21, antiderivative size = 360, 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 {x^3 \left (1000 d^2+180 d e+111 e^2\right )}{3 e^6}-\frac {x^2 \left (2000 d^3+450 d^2 e+444 d e^2+37 e^3\right )}{2 e^7}-\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 )}{3 e^9 (d+e x)^3}+\frac {2 x \left (1750 d^4+450 d^3 e+555 d^2 e^2+74 d e^3+74 e^4\right )}{e^8}+\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 )}{2 e^9 (d+e x)^2}-\frac {\left (5600 d^5+1575 d^4 e+2220 d^3 e^2+370 d^2 e^3+592 d e^4-65 e^5\right ) \log (d+e x)}{e^9}-\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^9 (d+e x)}-\frac {5 x^4 (80 d+9 e)}{4 e^5}+\frac {20 x^5}{e^4} \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)^4} \, dx &=\int \left (\frac {2 \left (1750 d^4+450 d^3 e+555 d^2 e^2+74 d e^3+74 e^4\right )}{e^8}-\frac {\left (2000 d^3+450 d^2 e+444 d e^2+37 e^3\right ) x}{e^7}+\frac {\left (1000 d^2+180 d e+111 e^2\right ) x^2}{e^6}-\frac {5 (80 d+9 e) x^3}{e^5}+\frac {100 x^4}{e^4}+\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)^4}+\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)^3}+\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)^2}+\frac {-5600 d^5-1575 d^4 e-2220 d^3 e^2-370 d^2 e^3-592 d e^4+65 e^5}{e^8 (d+e x)}\right ) \, dx\\ &=\frac {2 \left (1750 d^4+450 d^3 e+555 d^2 e^2+74 d e^3+74 e^4\right ) x}{e^8}-\frac {\left (2000 d^3+450 d^2 e+444 d e^2+37 e^3\right ) x^2}{2 e^7}+\frac {\left (1000 d^2+180 d e+111 e^2\right ) x^3}{3 e^6}-\frac {5 (80 d+9 e) x^4}{4 e^5}+\frac {20 x^5}{e^4}-\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 )}{3 e^9 (d+e x)^3}+\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 )}{2 e^9 (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^9 (d+e x)}-\frac {\left (5600 d^5+1575 d^4 e+2220 d^3 e^2+370 d^2 e^3+592 d e^4-65 e^5\right ) \log (d+e x)}{e^9}\\ \end {align*}
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Mathematica [A]
time = 0.08, size = 344, normalized size = 0.96 \begin {gather*} \frac {24 e \left (1750 d^4+450 d^3 e+555 d^2 e^2+74 d e^3+74 e^4\right ) x-6 e^2 \left (2000 d^3+450 d^2 e+444 d e^2+37 e^3\right ) x^2+4 e^3 \left (1000 d^2+180 d e+111 e^2\right ) x^3-15 e^4 (80 d+9 e) x^4+240 e^5 x^5-\frac {4 \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 )}{(d+e x)^3}+\frac {6 \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 )}{(d+e x)^2}-\frac {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}-12 \left (5600 d^5+1575 d^4 e+2220 d^3 e^2+370 d^2 e^3+592 d e^4-65 e^5\right ) \log (d+e x)}{12 e^9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 382, normalized size = 1.06
method | result | size |
norman | \(\frac {\frac {20 x^{8}}{e}-\frac {61600 d^{8}+17325 d^{7} e +24420 d^{6} e^{2}+4070 d^{5} e^{3}+6512 d^{4} e^{4}-715 d^{3} e^{5}+214 d^{2} e^{6}+33 d \,e^{7}+36 e^{8}}{6 e^{9}}-\frac {5 \left (32 d +9 e \right ) x^{7}}{4 e^{2}}+\frac {\left (1120 d^{2}+315 d e +444 e^{2}\right ) x^{6}}{12 e^{3}}-\frac {\left (1120 d^{3}+315 d^{2} e +444 d \,e^{2}+74 e^{3}\right ) x^{5}}{4 e^{4}}+\frac {\left (5600 d^{4}+1575 d^{3} e +2220 d^{2} e^{2}+370 d \,e^{3}+592 e^{4}\right ) x^{4}}{4 e^{5}}-\frac {\left (16800 d^{6}+4725 d^{5} e +6660 d^{4} e^{2}+1110 d^{3} e^{3}+1776 d^{2} e^{4}-195 d \,e^{5}+107 e^{6}\right ) x^{2}}{e^{7}}-\frac {\left (50400 d^{7}+14175 d^{6} e +19980 d^{5} e^{2}+3330 d^{4} e^{3}+5328 d^{3} e^{4}-585 d^{2} e^{5}+214 d \,e^{6}+33 e^{7}\right ) x}{2 e^{8}}}{\left (e x +d \right )^{3}}-\frac {\left (5600 d^{5}+1575 d^{4} e +2220 d^{3} e^{2}+370 d^{2} e^{3}+592 d \,e^{4}-65 e^{5}\right ) \ln \left (e x +d \right )}{e^{9}}\) | \(361\) |
default | \(\frac {\left (-5600 d^{5}-1575 d^{4} e -2220 d^{3} e^{2}-370 d^{2} e^{3}-592 d \,e^{4}+65 e^{5}\right ) \ln \left (e x +d \right )}{e^{9}}-\frac {-800 d^{7}-315 d^{6} e -666 d^{5} e^{2}-185 d^{4} e^{3}-592 d^{3} e^{4}+195 d^{2} e^{5}-214 d \,e^{6}+33 e^{7}}{2 e^{9} \left (e x +d \right )^{2}}-\frac {2800 d^{6}+945 d^{5} e +1665 d^{4} e^{2}+370 d^{3} e^{3}+888 d^{2} e^{4}-195 d \,e^{5}+107 e^{6}}{e^{9} \left (e x +d \right )}-\frac {100 d^{8}+45 d^{7} e +111 d^{6} e^{2}+37 d^{5} e^{3}+148 d^{4} e^{4}-65 d^{3} e^{5}+107 d^{2} e^{6}-33 d \,e^{7}+18 e^{8}}{3 e^{9} \left (e x +d \right )^{3}}+\frac {20 e^{4} x^{5}-100 d \,e^{3} x^{4}-\frac {45}{4} x^{4} e^{4}+\frac {1000}{3} d^{2} e^{2} x^{3}+60 d \,e^{3} x^{3}+37 e^{4} x^{3}-1000 d^{3} e \,x^{2}-225 d^{2} e^{2} x^{2}-222 d \,e^{3} x^{2}-\frac {37}{2} e^{4} x^{2}+3500 d^{4} x +900 d^{3} e x +1110 d^{2} e^{2} x +148 d \,e^{3} x +148 e^{4} x}{e^{8}}\) | \(382\) |
risch | \(\frac {20 x^{5}}{e^{4}}-\frac {100 d \,x^{4}}{e^{5}}-\frac {45 x^{4}}{4 e^{4}}+\frac {1000 d^{2} x^{3}}{3 e^{6}}+\frac {60 d \,x^{3}}{e^{5}}+\frac {37 x^{3}}{e^{4}}-\frac {1000 d^{3} x^{2}}{e^{7}}-\frac {225 d^{2} x^{2}}{e^{6}}-\frac {222 d \,x^{2}}{e^{5}}-\frac {37 x^{2}}{2 e^{4}}+\frac {3500 d^{4} x}{e^{8}}+\frac {900 d^{3} x}{e^{7}}+\frac {1110 d^{2} x}{e^{6}}+\frac {148 d x}{e^{5}}+\frac {148 x}{e^{4}}+\frac {\left (-2800 d^{6} e -945 d^{5} e^{2}-1665 d^{4} e^{3}-370 d^{3} e^{4}-888 d^{2} e^{5}+195 d \,e^{6}-107 e^{7}\right ) x^{2}+\left (-5200 d^{7}-\frac {3465}{2} d^{6} e -2997 d^{5} e^{2}-\frac {1295}{2} d^{4} e^{3}-1480 d^{3} e^{4}+\frac {585}{2} d^{2} e^{5}-107 d \,e^{6}-\frac {33}{2} e^{7}\right ) x -\frac {14600 d^{8}+4815 d^{7} e +8214 d^{6} e^{2}+1739 d^{5} e^{3}+3848 d^{4} e^{4}-715 d^{3} e^{5}+214 d^{2} e^{6}+33 d \,e^{7}+36 e^{8}}{6 e}}{e^{8} \left (e x +d \right )^{3}}-\frac {5600 \ln \left (e x +d \right ) d^{5}}{e^{9}}-\frac {1575 \ln \left (e x +d \right ) d^{4}}{e^{8}}-\frac {2220 \ln \left (e x +d \right ) d^{3}}{e^{7}}-\frac {370 \ln \left (e x +d \right ) d^{2}}{e^{6}}-\frac {592 \ln \left (e x +d \right ) d}{e^{5}}+\frac {65 \ln \left (e x +d \right )}{e^{4}}\) | \(404\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 353, normalized size = 0.98 \begin {gather*} -{\left (5600 \, d^{5} + 1575 \, d^{4} e + 2220 \, d^{3} e^{2} + 370 \, d^{2} e^{3} + 592 \, d e^{4} - 65 \, e^{5}\right )} e^{\left (-9\right )} \log \left (x e + d\right ) + \frac {1}{12} \, {\left (240 \, x^{5} e^{4} - 15 \, {\left (80 \, d e^{3} + 9 \, e^{4}\right )} x^{4} + 4 \, {\left (1000 \, d^{2} e^{2} + 180 \, d e^{3} + 111 \, e^{4}\right )} x^{3} - 6 \, {\left (2000 \, d^{3} e + 450 \, d^{2} e^{2} + 444 \, d e^{3} + 37 \, e^{4}\right )} x^{2} + 24 \, {\left (1750 \, d^{4} + 450 \, d^{3} e + 555 \, d^{2} e^{2} + 74 \, d e^{3} + 74 \, e^{4}\right )} x\right )} e^{\left (-8\right )} - \frac {14600 \, d^{8} + 4815 \, d^{7} e + 8214 \, d^{6} e^{2} + 1739 \, d^{5} e^{3} + 3848 \, d^{4} e^{4} - 715 \, d^{3} e^{5} + 6 \, {\left (2800 \, d^{6} e^{2} + 945 \, d^{5} e^{3} + 1665 \, d^{4} e^{4} + 370 \, d^{3} e^{5} + 888 \, d^{2} e^{6} - 195 \, d e^{7} + 107 \, e^{8}\right )} x^{2} + 214 \, d^{2} e^{6} + 3 \, {\left (10400 \, d^{7} e + 3465 \, d^{6} e^{2} + 5994 \, d^{5} e^{3} + 1295 \, d^{4} e^{4} + 2960 \, d^{3} e^{5} - 585 \, d^{2} e^{6} + 214 \, d e^{7} + 33 \, e^{8}\right )} x + 33 \, d e^{7} + 36 \, e^{8}}{6 \, {\left (x^{3} e^{12} + 3 \, d x^{2} e^{11} + 3 \, d^{2} x e^{10} + d^{3} 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 = 539, normalized size = 1.50 \begin {gather*} -\frac {29200 \, d^{8} - 3 \, {\left (80 \, x^{8} - 45 \, x^{7} + 148 \, x^{6} - 74 \, x^{5} + 592 \, x^{4} - 428 \, x^{2} - 66 \, x - 24\right )} e^{8} + 3 \, {\left (160 \, d x^{7} - 105 \, d x^{6} + 444 \, d x^{5} - 370 \, d x^{4} - 1776 \, d x^{3} - 780 \, d x^{2} + 428 \, d x + 22 \, d\right )} e^{7} - {\left (1120 \, d^{2} x^{6} - 945 \, d^{2} x^{5} + 6660 \, d^{2} x^{4} + 4662 \, d^{2} x^{3} - 5328 \, d^{2} x^{2} + 3510 \, d^{2} x - 428 \, d^{2}\right )} e^{6} + {\left (3360 \, d^{3} x^{5} - 4725 \, d^{3} x^{4} - 32412 \, d^{3} x^{3} - 666 \, d^{3} x^{2} + 15984 \, d^{3} x - 1430 \, d^{3}\right )} e^{5} - 2 \, {\left (8400 \, d^{4} x^{4} + 12510 \, d^{4} x^{3} + 8658 \, d^{4} x^{2} - 2997 \, d^{4} x - 3848 \, d^{4}\right )} e^{4} - 2 \, {\left (47000 \, d^{5} x^{3} + 9180 \, d^{5} x^{2} - 11322 \, d^{5} x - 1739 \, d^{5}\right )} e^{3} - 6 \, {\left (13400 \, d^{6} x^{2} - 1665 \, d^{6} x - 2738 \, d^{6}\right )} e^{2} + 30 \, {\left (680 \, d^{7} x + 321 \, d^{7}\right )} e + 12 \, {\left (5600 \, d^{8} - 65 \, x^{3} e^{8} + {\left (592 \, d x^{3} - 195 \, d x^{2}\right )} e^{7} + {\left (370 \, d^{2} x^{3} + 1776 \, d^{2} x^{2} - 195 \, d^{2} x\right )} e^{6} + {\left (2220 \, d^{3} x^{3} + 1110 \, d^{3} x^{2} + 1776 \, d^{3} x - 65 \, d^{3}\right )} e^{5} + {\left (1575 \, d^{4} x^{3} + 6660 \, d^{4} x^{2} + 1110 \, d^{4} x + 592 \, d^{4}\right )} e^{4} + 5 \, {\left (1120 \, d^{5} x^{3} + 945 \, d^{5} x^{2} + 1332 \, d^{5} x + 74 \, d^{5}\right )} e^{3} + 15 \, {\left (1120 \, d^{6} x^{2} + 315 \, d^{6} x + 148 \, d^{6}\right )} e^{2} + 525 \, {\left (32 \, d^{7} x + 3 \, d^{7}\right )} e\right )} \log \left (x e + d\right )}{12 \, {\left (x^{3} e^{12} + 3 \, d x^{2} e^{11} + 3 \, d^{2} x e^{10} + d^{3} e^{9}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 2.73, size = 401, normalized size = 1.11 \begin {gather*} x^{4} \left (- \frac {100 d}{e^{5}} - \frac {45}{4 e^{4}}\right ) + x^{3} \cdot \left (\frac {1000 d^{2}}{3 e^{6}} + \frac {60 d}{e^{5}} + \frac {37}{e^{4}}\right ) + x^{2} \left (- \frac {1000 d^{3}}{e^{7}} - \frac {225 d^{2}}{e^{6}} - \frac {222 d}{e^{5}} - \frac {37}{2 e^{4}}\right ) + x \left (\frac {3500 d^{4}}{e^{8}} + \frac {900 d^{3}}{e^{7}} + \frac {1110 d^{2}}{e^{6}} + \frac {148 d}{e^{5}} + \frac {148}{e^{4}}\right ) + \frac {- 14600 d^{8} - 4815 d^{7} e - 8214 d^{6} e^{2} - 1739 d^{5} e^{3} - 3848 d^{4} e^{4} + 715 d^{3} e^{5} - 214 d^{2} e^{6} - 33 d e^{7} - 36 e^{8} + x^{2} \left (- 16800 d^{6} e^{2} - 5670 d^{5} e^{3} - 9990 d^{4} e^{4} - 2220 d^{3} e^{5} - 5328 d^{2} e^{6} + 1170 d e^{7} - 642 e^{8}\right ) + x \left (- 31200 d^{7} e - 10395 d^{6} e^{2} - 17982 d^{5} e^{3} - 3885 d^{4} e^{4} - 8880 d^{3} e^{5} + 1755 d^{2} e^{6} - 642 d e^{7} - 99 e^{8}\right )}{6 d^{3} e^{9} + 18 d^{2} e^{10} x + 18 d e^{11} x^{2} + 6 e^{12} x^{3}} + \frac {20 x^{5}}{e^{4}} - \frac {\left (5600 d^{5} + 1575 d^{4} e + 2220 d^{3} e^{2} + 370 d^{2} e^{3} + 592 d e^{4} - 65 e^{5}\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 = 3.85, size = 345, normalized size = 0.96 \begin {gather*} -{\left (5600 \, d^{5} + 1575 \, d^{4} e + 2220 \, d^{3} e^{2} + 370 \, d^{2} e^{3} + 592 \, d e^{4} - 65 \, e^{5}\right )} e^{\left (-9\right )} \log \left ({\left | x e + d \right |}\right ) + \frac {1}{12} \, {\left (240 \, x^{5} e^{16} - 1200 \, d x^{4} e^{15} + 4000 \, d^{2} x^{3} e^{14} - 12000 \, d^{3} x^{2} e^{13} + 42000 \, d^{4} x e^{12} - 135 \, x^{4} e^{16} + 720 \, d x^{3} e^{15} - 2700 \, d^{2} x^{2} e^{14} + 10800 \, d^{3} x e^{13} + 444 \, x^{3} e^{16} - 2664 \, d x^{2} e^{15} + 13320 \, d^{2} x e^{14} - 222 \, x^{2} e^{16} + 1776 \, d x e^{15} + 1776 \, x e^{16}\right )} e^{\left (-20\right )} - \frac {{\left (14600 \, d^{8} + 4815 \, d^{7} e + 8214 \, d^{6} e^{2} + 1739 \, d^{5} e^{3} + 3848 \, d^{4} e^{4} - 715 \, d^{3} e^{5} + 6 \, {\left (2800 \, d^{6} e^{2} + 945 \, d^{5} e^{3} + 1665 \, d^{4} e^{4} + 370 \, d^{3} e^{5} + 888 \, d^{2} e^{6} - 195 \, d e^{7} + 107 \, e^{8}\right )} x^{2} + 214 \, d^{2} e^{6} + 3 \, {\left (10400 \, d^{7} e + 3465 \, d^{6} e^{2} + 5994 \, d^{5} e^{3} + 1295 \, d^{4} e^{4} + 2960 \, d^{3} e^{5} - 585 \, d^{2} e^{6} + 214 \, d e^{7} + 33 \, e^{8}\right )} x + 33 \, d e^{7} + 36 \, e^{8}\right )} e^{\left (-9\right )}}{6 \, {\left (x e + d\right )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.28, size = 560, normalized size = 1.56 \begin {gather*} x^3\,\left (\frac {37}{e^4}-\frac {200\,d^2}{e^6}+\frac {4\,d\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{3\,e}\right )-x^2\,\left (\frac {37}{2\,e^4}+\frac {200\,d^3}{e^7}+\frac {2\,d\,\left (\frac {111}{e^4}-\frac {600\,d^2}{e^6}+\frac {4\,d\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{e}\right )}{e}-\frac {3\,d^2\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{e^2}\right )-\frac {x\,\left (5200\,d^7+\frac {3465\,d^6\,e}{2}+2997\,d^5\,e^2+\frac {1295\,d^4\,e^3}{2}+1480\,d^3\,e^4-\frac {585\,d^2\,e^5}{2}+107\,d\,e^6+\frac {33\,e^7}{2}\right )+\frac {14600\,d^8+4815\,d^7\,e+8214\,d^6\,e^2+1739\,d^5\,e^3+3848\,d^4\,e^4-715\,d^3\,e^5+214\,d^2\,e^6+33\,d\,e^7+36\,e^8}{6\,e}+x^2\,\left (2800\,d^6\,e+945\,d^5\,e^2+1665\,d^4\,e^3+370\,d^3\,e^4+888\,d^2\,e^5-195\,d\,e^6+107\,e^7\right )}{d^3\,e^8+3\,d^2\,e^9\,x+3\,d\,e^{10}\,x^2+e^{11}\,x^3}-x^4\,\left (\frac {100\,d}{e^5}+\frac {45}{4\,e^4}\right )+x\,\left (\frac {148}{e^4}-\frac {100\,d^4}{e^8}+\frac {4\,d\,\left (\frac {37}{e^4}+\frac {400\,d^3}{e^7}+\frac {4\,d\,\left (\frac {111}{e^4}-\frac {600\,d^2}{e^6}+\frac {4\,d\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{e}\right )}{e}-\frac {6\,d^2\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{e^2}\right )}{e}-\frac {6\,d^2\,\left (\frac {111}{e^4}-\frac {600\,d^2}{e^6}+\frac {4\,d\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{e}\right )}{e^2}+\frac {4\,d^3\,\left (\frac {400\,d}{e^5}+\frac {45}{e^4}\right )}{e^3}\right )+\frac {20\,x^5}{e^4}-\frac {\ln \left (d+e\,x\right )\,\left (5600\,d^5+1575\,d^4\,e+2220\,d^3\,e^2+370\,d^2\,e^3+592\,d\,e^4-65\,e^5\right )}{e^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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