Optimal. Leaf size=308 \[ -\frac {2 b^5 (d+e x)^{15/2} (-6 a B e-A b e+7 b B d)}{15 e^8}+\frac {6 b^4 (d+e x)^{13/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{13 e^8}-\frac {10 b^3 (d+e x)^{11/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{11 e^8}+\frac {10 b^2 (d+e x)^{9/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{9 e^8}-\frac {6 b (d+e x)^{7/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{7 e^8}+\frac {2 (d+e x)^{5/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{5 e^8}-\frac {2 (d+e x)^{3/2} (b d-a e)^6 (B d-A e)}{3 e^8}+\frac {2 b^6 B (d+e x)^{17/2}}{17 e^8} \]
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Rubi [A] time = 0.14, antiderivative size = 308, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {27, 77} \begin {gather*} -\frac {2 b^5 (d+e x)^{15/2} (-6 a B e-A b e+7 b B d)}{15 e^8}+\frac {6 b^4 (d+e x)^{13/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{13 e^8}-\frac {10 b^3 (d+e x)^{11/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{11 e^8}+\frac {10 b^2 (d+e x)^{9/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{9 e^8}-\frac {6 b (d+e x)^{7/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{7 e^8}+\frac {2 (d+e x)^{5/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{5 e^8}-\frac {2 (d+e x)^{3/2} (b d-a e)^6 (B d-A e)}{3 e^8}+\frac {2 b^6 B (d+e x)^{17/2}}{17 e^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 77
Rubi steps
\begin {align*} \int (A+B x) \sqrt {d+e x} \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx &=\int (a+b x)^6 (A+B x) \sqrt {d+e x} \, dx\\ &=\int \left (\frac {(-b d+a e)^6 (-B d+A e) \sqrt {d+e x}}{e^7}+\frac {(-b d+a e)^5 (-7 b B d+6 A b e+a B e) (d+e x)^{3/2}}{e^7}+\frac {3 b (b d-a e)^4 (-7 b B d+5 A b e+2 a B e) (d+e x)^{5/2}}{e^7}-\frac {5 b^2 (b d-a e)^3 (-7 b B d+4 A b e+3 a B e) (d+e x)^{7/2}}{e^7}+\frac {5 b^3 (b d-a e)^2 (-7 b B d+3 A b e+4 a B e) (d+e x)^{9/2}}{e^7}-\frac {3 b^4 (b d-a e) (-7 b B d+2 A b e+5 a B e) (d+e x)^{11/2}}{e^7}+\frac {b^5 (-7 b B d+A b e+6 a B e) (d+e x)^{13/2}}{e^7}+\frac {b^6 B (d+e x)^{15/2}}{e^7}\right ) \, dx\\ &=-\frac {2 (b d-a e)^6 (B d-A e) (d+e x)^{3/2}}{3 e^8}+\frac {2 (b d-a e)^5 (7 b B d-6 A b e-a B e) (d+e x)^{5/2}}{5 e^8}-\frac {6 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e) (d+e x)^{7/2}}{7 e^8}+\frac {10 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e) (d+e x)^{9/2}}{9 e^8}-\frac {10 b^3 (b d-a e)^2 (7 b B d-3 A b e-4 a B e) (d+e x)^{11/2}}{11 e^8}+\frac {6 b^4 (b d-a e) (7 b B d-2 A b e-5 a B e) (d+e x)^{13/2}}{13 e^8}-\frac {2 b^5 (7 b B d-A b e-6 a B e) (d+e x)^{15/2}}{15 e^8}+\frac {2 b^6 B (d+e x)^{17/2}}{17 e^8}\\ \end {align*}
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Mathematica [A] time = 0.24, size = 259, normalized size = 0.84 \begin {gather*} \frac {2 (d+e x)^{3/2} \left (-51051 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+176715 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-348075 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+425425 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)-328185 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)+153153 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)-255255 (b d-a e)^6 (B d-A e)+45045 b^6 B (d+e x)^7\right )}{765765 e^8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [B] time = 0.40, size = 1069, normalized size = 3.47 \begin {gather*} \frac {2 (d+e x)^{3/2} \left (-255255 b^6 B d^7+255255 A b^6 e d^6+1531530 a b^5 B e d^6+1072071 b^6 B (d+e x) d^6-1531530 a A b^5 e^2 d^5-3828825 a^2 b^4 B e^2 d^5-2297295 b^6 B (d+e x)^2 d^5-918918 A b^6 e (d+e x) d^5-5513508 a b^5 B e (d+e x) d^5+3828825 a^2 A b^4 e^3 d^4+5105100 a^3 b^3 B e^3 d^4+2977975 b^6 B (d+e x)^3 d^4+1640925 A b^6 e (d+e x)^2 d^4+9845550 a b^5 B e (d+e x)^2 d^4+4594590 a A b^5 e^2 (d+e x) d^4+11486475 a^2 b^4 B e^2 (d+e x) d^4-5105100 a^3 A b^3 e^4 d^3-3828825 a^4 b^2 B e^4 d^3-2436525 b^6 B (d+e x)^4 d^3-1701700 A b^6 e (d+e x)^3 d^3-10210200 a b^5 B e (d+e x)^3 d^3-6563700 a A b^5 e^2 (d+e x)^2 d^3-16409250 a^2 b^4 B e^2 (d+e x)^2 d^3-9189180 a^2 A b^4 e^3 (d+e x) d^3-12252240 a^3 b^3 B e^3 (d+e x) d^3+3828825 a^4 A b^2 e^5 d^2+1531530 a^5 b B e^5 d^2+1237005 b^6 B (d+e x)^5 d^2+1044225 A b^6 e (d+e x)^4 d^2+6265350 a b^5 B e (d+e x)^4 d^2+5105100 a A b^5 e^2 (d+e x)^3 d^2+12762750 a^2 b^4 B e^2 (d+e x)^3 d^2+9845550 a^2 A b^4 e^3 (d+e x)^2 d^2+13127400 a^3 b^3 B e^3 (d+e x)^2 d^2+9189180 a^3 A b^3 e^4 (d+e x) d^2+6891885 a^4 b^2 B e^4 (d+e x) d^2-1531530 a^5 A b e^6 d-255255 a^6 B e^6 d-357357 b^6 B (d+e x)^6 d-353430 A b^6 e (d+e x)^5 d-2120580 a b^5 B e (d+e x)^5 d-2088450 a A b^5 e^2 (d+e x)^4 d-5221125 a^2 b^4 B e^2 (d+e x)^4 d-5105100 a^2 A b^4 e^3 (d+e x)^3 d-6806800 a^3 b^3 B e^3 (d+e x)^3 d-6563700 a^3 A b^3 e^4 (d+e x)^2 d-4922775 a^4 b^2 B e^4 (d+e x)^2 d-4594590 a^4 A b^2 e^5 (d+e x) d-1837836 a^5 b B e^5 (d+e x) d+255255 a^6 A e^7+45045 b^6 B (d+e x)^7+51051 A b^6 e (d+e x)^6+306306 a b^5 B e (d+e x)^6+353430 a A b^5 e^2 (d+e x)^5+883575 a^2 b^4 B e^2 (d+e x)^5+1044225 a^2 A b^4 e^3 (d+e x)^4+1392300 a^3 b^3 B e^3 (d+e x)^4+1701700 a^3 A b^3 e^4 (d+e x)^3+1276275 a^4 b^2 B e^4 (d+e x)^3+1640925 a^4 A b^2 e^5 (d+e x)^2+656370 a^5 b B e^5 (d+e x)^2+918918 a^5 A b e^6 (d+e x)+153153 a^6 B e^6 (d+e x)\right )}{765765 e^8} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 942, normalized size = 3.06 \begin {gather*} \frac {2 \, {\left (45045 \, B b^{6} e^{8} x^{8} - 14336 \, B b^{6} d^{8} + 255255 \, A a^{6} d e^{7} + 17408 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{7} e - 65280 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{6} e^{2} + 141440 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{5} e^{3} - 194480 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{4} e^{4} + 175032 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{3} e^{5} - 102102 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d^{2} e^{6} + 3003 \, {\left (B b^{6} d e^{7} + 17 \, {\left (6 \, B a b^{5} + A b^{6}\right )} e^{8}\right )} x^{7} - 231 \, {\left (14 \, B b^{6} d^{2} e^{6} - 17 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e^{7} - 765 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{8}\right )} x^{6} + 63 \, {\left (56 \, B b^{6} d^{3} e^{5} - 68 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{6} + 255 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{7} + 5525 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{8}\right )} x^{5} - 35 \, {\left (112 \, B b^{6} d^{4} e^{4} - 136 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{5} + 510 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{6} - 1105 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{7} - 12155 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{8}\right )} x^{4} + 5 \, {\left (896 \, B b^{6} d^{5} e^{3} - 1088 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e^{4} + 4080 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{5} - 8840 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{6} + 12155 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{7} + 65637 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{8}\right )} x^{3} - 3 \, {\left (1792 \, B b^{6} d^{6} e^{2} - 2176 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e^{3} + 8160 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{4} - 17680 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{5} + 24310 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{6} - 21879 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{7} - 51051 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{8}\right )} x^{2} + {\left (7168 \, B b^{6} d^{7} e + 255255 \, A a^{6} e^{8} - 8704 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e^{2} + 32640 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{3} - 70720 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{4} + 97240 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{5} - 87516 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{6} + 51051 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{7}\right )} x\right )} \sqrt {e x + d}}{765765 \, e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.29, size = 1984, normalized size = 6.44
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 913, normalized size = 2.96 \begin {gather*} \frac {2 \left (e x +d \right )^{\frac {3}{2}} \left (45045 B \,b^{6} x^{7} e^{7}+51051 A \,b^{6} e^{7} x^{6}+306306 B a \,b^{5} e^{7} x^{6}-42042 B \,b^{6} d \,e^{6} x^{6}+353430 A a \,b^{5} e^{7} x^{5}-47124 A \,b^{6} d \,e^{6} x^{5}+883575 B \,a^{2} b^{4} e^{7} x^{5}-282744 B a \,b^{5} d \,e^{6} x^{5}+38808 B \,b^{6} d^{2} e^{5} x^{5}+1044225 A \,a^{2} b^{4} e^{7} x^{4}-321300 A a \,b^{5} d \,e^{6} x^{4}+42840 A \,b^{6} d^{2} e^{5} x^{4}+1392300 B \,a^{3} b^{3} e^{7} x^{4}-803250 B \,a^{2} b^{4} d \,e^{6} x^{4}+257040 B a \,b^{5} d^{2} e^{5} x^{4}-35280 B \,b^{6} d^{3} e^{4} x^{4}+1701700 A \,a^{3} b^{3} e^{7} x^{3}-928200 A \,a^{2} b^{4} d \,e^{6} x^{3}+285600 A a \,b^{5} d^{2} e^{5} x^{3}-38080 A \,b^{6} d^{3} e^{4} x^{3}+1276275 B \,a^{4} b^{2} e^{7} x^{3}-1237600 B \,a^{3} b^{3} d \,e^{6} x^{3}+714000 B \,a^{2} b^{4} d^{2} e^{5} x^{3}-228480 B a \,b^{5} d^{3} e^{4} x^{3}+31360 B \,b^{6} d^{4} e^{3} x^{3}+1640925 A \,a^{4} b^{2} e^{7} x^{2}-1458600 A \,a^{3} b^{3} d \,e^{6} x^{2}+795600 A \,a^{2} b^{4} d^{2} e^{5} x^{2}-244800 A a \,b^{5} d^{3} e^{4} x^{2}+32640 A \,b^{6} d^{4} e^{3} x^{2}+656370 B \,a^{5} b \,e^{7} x^{2}-1093950 B \,a^{4} b^{2} d \,e^{6} x^{2}+1060800 B \,a^{3} b^{3} d^{2} e^{5} x^{2}-612000 B \,a^{2} b^{4} d^{3} e^{4} x^{2}+195840 B a \,b^{5} d^{4} e^{3} x^{2}-26880 B \,b^{6} d^{5} e^{2} x^{2}+918918 A \,a^{5} b \,e^{7} x -1312740 A \,a^{4} b^{2} d \,e^{6} x +1166880 A \,a^{3} b^{3} d^{2} e^{5} x -636480 A \,a^{2} b^{4} d^{3} e^{4} x +195840 A a \,b^{5} d^{4} e^{3} x -26112 A \,b^{6} d^{5} e^{2} x +153153 B \,a^{6} e^{7} x -525096 B \,a^{5} b d \,e^{6} x +875160 B \,a^{4} b^{2} d^{2} e^{5} x -848640 B \,a^{3} b^{3} d^{3} e^{4} x +489600 B \,a^{2} b^{4} d^{4} e^{3} x -156672 B a \,b^{5} d^{5} e^{2} x +21504 B \,b^{6} d^{6} e x +255255 A \,a^{6} e^{7}-612612 A \,a^{5} b d \,e^{6}+875160 A \,a^{4} b^{2} d^{2} e^{5}-777920 A \,a^{3} b^{3} d^{3} e^{4}+424320 A \,a^{2} b^{4} d^{4} e^{3}-130560 A a \,b^{5} d^{5} e^{2}+17408 A \,b^{6} d^{6} e -102102 B \,a^{6} d \,e^{6}+350064 B \,a^{5} b \,d^{2} e^{5}-583440 B \,a^{4} b^{2} d^{3} e^{4}+565760 B \,a^{3} b^{3} d^{4} e^{3}-326400 B \,a^{2} b^{4} d^{5} e^{2}+104448 B a \,b^{5} d^{6} e -14336 B \,b^{6} d^{7}\right )}{765765 e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.65, size = 767, normalized size = 2.49 \begin {gather*} \frac {2 \, {\left (45045 \, {\left (e x + d\right )}^{\frac {17}{2}} B b^{6} - 51051 \, {\left (7 \, B b^{6} d - {\left (6 \, B a b^{5} + A b^{6}\right )} e\right )} {\left (e x + d\right )}^{\frac {15}{2}} + 176715 \, {\left (7 \, B b^{6} d^{2} - 2 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e + {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{2}\right )} {\left (e x + d\right )}^{\frac {13}{2}} - 348075 \, {\left (7 \, B b^{6} d^{3} - 3 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{2} - {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{3}\right )} {\left (e x + d\right )}^{\frac {11}{2}} + 425425 \, {\left (7 \, B b^{6} d^{4} - 4 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e + 6 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{2} - 4 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{3} + {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{4}\right )} {\left (e x + d\right )}^{\frac {9}{2}} - 328185 \, {\left (7 \, B b^{6} d^{5} - 5 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e + 10 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{2} - 10 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{4} - {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{5}\right )} {\left (e x + d\right )}^{\frac {7}{2}} + 153153 \, {\left (7 \, B b^{6} d^{6} - 6 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e + 15 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{2} - 20 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{3} + 15 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{4} - 6 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{5} + {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{6}\right )} {\left (e x + d\right )}^{\frac {5}{2}} - 255255 \, {\left (B b^{6} d^{7} - A a^{6} e^{7} - {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 3 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} - 5 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 5 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} - 3 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} + {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6}\right )} {\left (e x + d\right )}^{\frac {3}{2}}\right )}}{765765 \, e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.93, size = 279, normalized size = 0.91 \begin {gather*} \frac {{\left (d+e\,x\right )}^{15/2}\,\left (2\,A\,b^6\,e-14\,B\,b^6\,d+12\,B\,a\,b^5\,e\right )}{15\,e^8}+\frac {2\,{\left (a\,e-b\,d\right )}^5\,{\left (d+e\,x\right )}^{5/2}\,\left (6\,A\,b\,e+B\,a\,e-7\,B\,b\,d\right )}{5\,e^8}+\frac {2\,B\,b^6\,{\left (d+e\,x\right )}^{17/2}}{17\,e^8}+\frac {2\,\left (A\,e-B\,d\right )\,{\left (a\,e-b\,d\right )}^6\,{\left (d+e\,x\right )}^{3/2}}{3\,e^8}+\frac {6\,b\,{\left (a\,e-b\,d\right )}^4\,{\left (d+e\,x\right )}^{7/2}\,\left (5\,A\,b\,e+2\,B\,a\,e-7\,B\,b\,d\right )}{7\,e^8}+\frac {6\,b^4\,\left (a\,e-b\,d\right )\,{\left (d+e\,x\right )}^{13/2}\,\left (2\,A\,b\,e+5\,B\,a\,e-7\,B\,b\,d\right )}{13\,e^8}+\frac {10\,b^2\,{\left (a\,e-b\,d\right )}^3\,{\left (d+e\,x\right )}^{9/2}\,\left (4\,A\,b\,e+3\,B\,a\,e-7\,B\,b\,d\right )}{9\,e^8}+\frac {10\,b^3\,{\left (a\,e-b\,d\right )}^2\,{\left (d+e\,x\right )}^{11/2}\,\left (3\,A\,b\,e+4\,B\,a\,e-7\,B\,b\,d\right )}{11\,e^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 13.35, size = 969, normalized size = 3.15 \begin {gather*} \frac {2 \left (\frac {B b^{6} \left (d + e x\right )^{\frac {17}{2}}}{17 e^{7}} + \frac {\left (d + e x\right )^{\frac {15}{2}} \left (A b^{6} e + 6 B a b^{5} e - 7 B b^{6} d\right )}{15 e^{7}} + \frac {\left (d + e x\right )^{\frac {13}{2}} \left (6 A a b^{5} e^{2} - 6 A b^{6} d e + 15 B a^{2} b^{4} e^{2} - 36 B a b^{5} d e + 21 B b^{6} d^{2}\right )}{13 e^{7}} + \frac {\left (d + e x\right )^{\frac {11}{2}} \left (15 A a^{2} b^{4} e^{3} - 30 A a b^{5} d e^{2} + 15 A b^{6} d^{2} e + 20 B a^{3} b^{3} e^{3} - 75 B a^{2} b^{4} d e^{2} + 90 B a b^{5} d^{2} e - 35 B b^{6} d^{3}\right )}{11 e^{7}} + \frac {\left (d + e x\right )^{\frac {9}{2}} \left (20 A a^{3} b^{3} e^{4} - 60 A a^{2} b^{4} d e^{3} + 60 A a b^{5} d^{2} e^{2} - 20 A b^{6} d^{3} e + 15 B a^{4} b^{2} e^{4} - 80 B a^{3} b^{3} d e^{3} + 150 B a^{2} b^{4} d^{2} e^{2} - 120 B a b^{5} d^{3} e + 35 B b^{6} d^{4}\right )}{9 e^{7}} + \frac {\left (d + e x\right )^{\frac {7}{2}} \left (15 A a^{4} b^{2} e^{5} - 60 A a^{3} b^{3} d e^{4} + 90 A a^{2} b^{4} d^{2} e^{3} - 60 A a b^{5} d^{3} e^{2} + 15 A b^{6} d^{4} e + 6 B a^{5} b e^{5} - 45 B a^{4} b^{2} d e^{4} + 120 B a^{3} b^{3} d^{2} e^{3} - 150 B a^{2} b^{4} d^{3} e^{2} + 90 B a b^{5} d^{4} e - 21 B b^{6} d^{5}\right )}{7 e^{7}} + \frac {\left (d + e x\right )^{\frac {5}{2}} \left (6 A a^{5} b e^{6} - 30 A a^{4} b^{2} d e^{5} + 60 A a^{3} b^{3} d^{2} e^{4} - 60 A a^{2} b^{4} d^{3} e^{3} + 30 A a b^{5} d^{4} e^{2} - 6 A b^{6} d^{5} e + B a^{6} e^{6} - 12 B a^{5} b d e^{5} + 45 B a^{4} b^{2} d^{2} e^{4} - 80 B a^{3} b^{3} d^{3} e^{3} + 75 B a^{2} b^{4} d^{4} e^{2} - 36 B a b^{5} d^{5} e + 7 B b^{6} d^{6}\right )}{5 e^{7}} + \frac {\left (d + e x\right )^{\frac {3}{2}} \left (A a^{6} e^{7} - 6 A a^{5} b d e^{6} + 15 A a^{4} b^{2} d^{2} e^{5} - 20 A a^{3} b^{3} d^{3} e^{4} + 15 A a^{2} b^{4} d^{4} e^{3} - 6 A a b^{5} d^{5} e^{2} + A b^{6} d^{6} e - B a^{6} d e^{6} + 6 B a^{5} b d^{2} e^{5} - 15 B a^{4} b^{2} d^{3} e^{4} + 20 B a^{3} b^{3} d^{4} e^{3} - 15 B a^{2} b^{4} d^{5} e^{2} + 6 B a b^{5} d^{6} e - B b^{6} d^{7}\right )}{3 e^{7}}\right )}{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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