Optimal. Leaf size=304 \[ -\frac {2 b^5 (d+e x)^{7/2} (-6 a B e-A b e+7 b B d)}{7 e^8}+\frac {6 b^4 (d+e x)^{5/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{5 e^8}-\frac {10 b^3 (d+e x)^{3/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac {10 b^2 \sqrt {d+e x} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8}+\frac {6 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8 \sqrt {d+e x}}-\frac {2 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8 (d+e x)^{3/2}}+\frac {2 (b d-a e)^6 (B d-A e)}{5 e^8 (d+e x)^{5/2}}+\frac {2 b^6 B (d+e x)^{9/2}}{9 e^8} \]
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Rubi [A] time = 0.15, antiderivative size = 304, 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)^{7/2} (-6 a B e-A b e+7 b B d)}{7 e^8}+\frac {6 b^4 (d+e x)^{5/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{5 e^8}-\frac {10 b^3 (d+e x)^{3/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac {10 b^2 \sqrt {d+e x} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8}+\frac {6 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8 \sqrt {d+e x}}-\frac {2 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8 (d+e x)^{3/2}}+\frac {2 (b d-a e)^6 (B d-A e)}{5 e^8 (d+e x)^{5/2}}+\frac {2 b^6 B (d+e x)^{9/2}}{9 e^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 77
Rubi steps
\begin {align*} \int \frac {(A+B x) \left (a^2+2 a b x+b^2 x^2\right )^3}{(d+e x)^{7/2}} \, dx &=\int \frac {(a+b x)^6 (A+B x)}{(d+e x)^{7/2}} \, dx\\ &=\int \left (\frac {(-b d+a e)^6 (-B d+A e)}{e^7 (d+e x)^{7/2}}+\frac {(-b d+a e)^5 (-7 b B d+6 A b e+a B e)}{e^7 (d+e x)^{5/2}}+\frac {3 b (b d-a e)^4 (-7 b B d+5 A b e+2 a B e)}{e^7 (d+e x)^{3/2}}-\frac {5 b^2 (b d-a e)^3 (-7 b B d+4 A b e+3 a B e)}{e^7 \sqrt {d+e x}}+\frac {5 b^3 (b d-a e)^2 (-7 b B d+3 A b e+4 a B e) \sqrt {d+e x}}{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)^{3/2}}{e^7}+\frac {b^5 (-7 b B d+A b e+6 a B e) (d+e x)^{5/2}}{e^7}+\frac {b^6 B (d+e x)^{7/2}}{e^7}\right ) \, dx\\ &=\frac {2 (b d-a e)^6 (B d-A e)}{5 e^8 (d+e x)^{5/2}}-\frac {2 (b d-a e)^5 (7 b B d-6 A b e-a B e)}{3 e^8 (d+e x)^{3/2}}+\frac {6 b (b d-a e)^4 (7 b B d-5 A b e-2 a B e)}{e^8 \sqrt {d+e x}}+\frac {10 b^2 (b d-a e)^3 (7 b B d-4 A b e-3 a B e) \sqrt {d+e x}}{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)^{3/2}}{3 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)^{5/2}}{5 e^8}-\frac {2 b^5 (7 b B d-A b e-6 a B e) (d+e x)^{7/2}}{7 e^8}+\frac {2 b^6 B (d+e x)^{9/2}}{9 e^8}\\ \end {align*}
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Mathematica [A] time = 0.19, size = 259, normalized size = 0.85 \begin {gather*} \frac {2 \left (-45 b^5 (d+e x)^6 (-6 a B e-A b e+7 b B d)+189 b^4 (d+e x)^5 (b d-a e) (-5 a B e-2 A b e+7 b B d)-525 b^3 (d+e x)^4 (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)+1575 b^2 (d+e x)^3 (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)+945 b (d+e x)^2 (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)-105 (d+e x) (b d-a e)^5 (-a B e-6 A b e+7 b B d)+63 (b d-a e)^6 (B d-A e)+35 b^6 B (d+e x)^7\right )}{315 e^8 (d+e x)^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [B] time = 0.23, size = 1069, normalized size = 3.52 \begin {gather*} \frac {2 \left (63 b^6 B d^7-63 A b^6 e d^6-378 a b^5 B e d^6-735 b^6 B (d+e x) d^6+378 a A b^5 e^2 d^5+945 a^2 b^4 B e^2 d^5+6615 b^6 B (d+e x)^2 d^5+630 A b^6 e (d+e x) d^5+3780 a b^5 B e (d+e x) d^5-945 a^2 A b^4 e^3 d^4-1260 a^3 b^3 B e^3 d^4+11025 b^6 B (d+e x)^3 d^4-4725 A b^6 e (d+e x)^2 d^4-28350 a b^5 B e (d+e x)^2 d^4-3150 a A b^5 e^2 (d+e x) d^4-7875 a^2 b^4 B e^2 (d+e x) d^4+1260 a^3 A b^3 e^4 d^3+945 a^4 b^2 B e^4 d^3-3675 b^6 B (d+e x)^4 d^3-6300 A b^6 e (d+e x)^3 d^3-37800 a b^5 B e (d+e x)^3 d^3+18900 a A b^5 e^2 (d+e x)^2 d^3+47250 a^2 b^4 B e^2 (d+e x)^2 d^3+6300 a^2 A b^4 e^3 (d+e x) d^3+8400 a^3 b^3 B e^3 (d+e x) d^3-945 a^4 A b^2 e^5 d^2-378 a^5 b B e^5 d^2+1323 b^6 B (d+e x)^5 d^2+1575 A b^6 e (d+e x)^4 d^2+9450 a b^5 B e (d+e x)^4 d^2+18900 a A b^5 e^2 (d+e x)^3 d^2+47250 a^2 b^4 B e^2 (d+e x)^3 d^2-28350 a^2 A b^4 e^3 (d+e x)^2 d^2-37800 a^3 b^3 B e^3 (d+e x)^2 d^2-6300 a^3 A b^3 e^4 (d+e x) d^2-4725 a^4 b^2 B e^4 (d+e x) d^2+378 a^5 A b e^6 d+63 a^6 B e^6 d-315 b^6 B (d+e x)^6 d-378 A b^6 e (d+e x)^5 d-2268 a b^5 B e (d+e x)^5 d-3150 a A b^5 e^2 (d+e x)^4 d-7875 a^2 b^4 B e^2 (d+e x)^4 d-18900 a^2 A b^4 e^3 (d+e x)^3 d-25200 a^3 b^3 B e^3 (d+e x)^3 d+18900 a^3 A b^3 e^4 (d+e x)^2 d+14175 a^4 b^2 B e^4 (d+e x)^2 d+3150 a^4 A b^2 e^5 (d+e x) d+1260 a^5 b B e^5 (d+e x) d-63 a^6 A e^7+35 b^6 B (d+e x)^7+45 A b^6 e (d+e x)^6+270 a b^5 B e (d+e x)^6+378 a A b^5 e^2 (d+e x)^5+945 a^2 b^4 B e^2 (d+e x)^5+1575 a^2 A b^4 e^3 (d+e x)^4+2100 a^3 b^3 B e^3 (d+e x)^4+6300 a^3 A b^3 e^4 (d+e x)^3+4725 a^4 b^2 B e^4 (d+e x)^3-4725 a^4 A b^2 e^5 (d+e x)^2-1890 a^5 b B e^5 (d+e x)^2-630 a^5 A b e^6 (d+e x)-105 a^6 B e^6 (d+e x)\right )}{315 e^8 (d+e x)^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.44, size = 802, normalized size = 2.64 \begin {gather*} \frac {2 \, {\left (35 \, B b^{6} e^{7} x^{7} + 14336 \, B b^{6} d^{7} - 63 \, A a^{6} e^{7} - 9216 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 16128 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} - 13440 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 5040 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} - 504 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} - 42 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6} - 5 \, {\left (14 \, B b^{6} d e^{6} - 9 \, {\left (6 \, B a b^{5} + A b^{6}\right )} e^{7}\right )} x^{6} + 3 \, {\left (56 \, B b^{6} d^{2} e^{5} - 36 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d e^{6} + 63 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} e^{7}\right )} x^{5} - 5 \, {\left (112 \, B b^{6} d^{3} e^{4} - 72 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{2} e^{5} + 126 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d e^{6} - 105 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} e^{7}\right )} x^{4} + 5 \, {\left (896 \, B b^{6} d^{4} e^{3} - 576 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{3} e^{4} + 1008 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{2} e^{5} - 840 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d e^{6} + 315 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} e^{7}\right )} x^{3} + 15 \, {\left (1792 \, B b^{6} d^{5} e^{2} - 1152 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{4} e^{3} + 2016 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{3} e^{4} - 1680 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{2} e^{5} + 630 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d e^{6} - 63 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} e^{7}\right )} x^{2} + 5 \, {\left (7168 \, B b^{6} d^{6} e - 4608 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{5} e^{2} + 8064 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{4} e^{3} - 6720 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{3} e^{4} + 2520 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{2} e^{5} - 252 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d e^{6} - 21 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} e^{7}\right )} x\right )} \sqrt {e x + d}}{315 \, {\left (e^{11} x^{3} + 3 \, d e^{10} x^{2} + 3 \, d^{2} e^{9} x + d^{3} e^{8}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.33, size = 1103, normalized size = 3.63
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 913, normalized size = 3.00 \begin {gather*} -\frac {2 \left (-35 B \,b^{6} x^{7} e^{7}-45 A \,b^{6} e^{7} x^{6}-270 B a \,b^{5} e^{7} x^{6}+70 B \,b^{6} d \,e^{6} x^{6}-378 A a \,b^{5} e^{7} x^{5}+108 A \,b^{6} d \,e^{6} x^{5}-945 B \,a^{2} b^{4} e^{7} x^{5}+648 B a \,b^{5} d \,e^{6} x^{5}-168 B \,b^{6} d^{2} e^{5} x^{5}-1575 A \,a^{2} b^{4} e^{7} x^{4}+1260 A a \,b^{5} d \,e^{6} x^{4}-360 A \,b^{6} d^{2} e^{5} x^{4}-2100 B \,a^{3} b^{3} e^{7} x^{4}+3150 B \,a^{2} b^{4} d \,e^{6} x^{4}-2160 B a \,b^{5} d^{2} e^{5} x^{4}+560 B \,b^{6} d^{3} e^{4} x^{4}-6300 A \,a^{3} b^{3} e^{7} x^{3}+12600 A \,a^{2} b^{4} d \,e^{6} x^{3}-10080 A a \,b^{5} d^{2} e^{5} x^{3}+2880 A \,b^{6} d^{3} e^{4} x^{3}-4725 B \,a^{4} b^{2} e^{7} x^{3}+16800 B \,a^{3} b^{3} d \,e^{6} x^{3}-25200 B \,a^{2} b^{4} d^{2} e^{5} x^{3}+17280 B a \,b^{5} d^{3} e^{4} x^{3}-4480 B \,b^{6} d^{4} e^{3} x^{3}+4725 A \,a^{4} b^{2} e^{7} x^{2}-37800 A \,a^{3} b^{3} d \,e^{6} x^{2}+75600 A \,a^{2} b^{4} d^{2} e^{5} x^{2}-60480 A a \,b^{5} d^{3} e^{4} x^{2}+17280 A \,b^{6} d^{4} e^{3} x^{2}+1890 B \,a^{5} b \,e^{7} x^{2}-28350 B \,a^{4} b^{2} d \,e^{6} x^{2}+100800 B \,a^{3} b^{3} d^{2} e^{5} x^{2}-151200 B \,a^{2} b^{4} d^{3} e^{4} x^{2}+103680 B a \,b^{5} d^{4} e^{3} x^{2}-26880 B \,b^{6} d^{5} e^{2} x^{2}+630 A \,a^{5} b \,e^{7} x +6300 A \,a^{4} b^{2} d \,e^{6} x -50400 A \,a^{3} b^{3} d^{2} e^{5} x +100800 A \,a^{2} b^{4} d^{3} e^{4} x -80640 A a \,b^{5} d^{4} e^{3} x +23040 A \,b^{6} d^{5} e^{2} x +105 B \,a^{6} e^{7} x +2520 B \,a^{5} b d \,e^{6} x -37800 B \,a^{4} b^{2} d^{2} e^{5} x +134400 B \,a^{3} b^{3} d^{3} e^{4} x -201600 B \,a^{2} b^{4} d^{4} e^{3} x +138240 B a \,b^{5} d^{5} e^{2} x -35840 B \,b^{6} d^{6} e x +63 A \,a^{6} e^{7}+252 A \,a^{5} b d \,e^{6}+2520 A \,a^{4} b^{2} d^{2} e^{5}-20160 A \,a^{3} b^{3} d^{3} e^{4}+40320 A \,a^{2} b^{4} d^{4} e^{3}-32256 A a \,b^{5} d^{5} e^{2}+9216 A \,b^{6} d^{6} e +42 B \,a^{6} d \,e^{6}+1008 B \,a^{5} b \,d^{2} e^{5}-15120 B \,a^{4} b^{2} d^{3} e^{4}+53760 B \,a^{3} b^{3} d^{4} e^{3}-80640 B \,a^{2} b^{4} d^{5} e^{2}+55296 B a \,b^{5} d^{6} e -14336 B \,b^{6} d^{7}\right )}{315 \left (e x +d \right )^{\frac {5}{2}} e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.63, size = 775, normalized size = 2.55 \begin {gather*} \frac {2 \, {\left (\frac {35 \, {\left (e x + d\right )}^{\frac {9}{2}} B b^{6} - 45 \, {\left (7 \, B b^{6} d - {\left (6 \, B a b^{5} + A b^{6}\right )} e\right )} {\left (e x + d\right )}^{\frac {7}{2}} + 189 \, {\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 {5}{2}} - 525 \, {\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 {3}{2}} + 1575 \, {\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 )} \sqrt {e x + d}}{e^{7}} + \frac {21 \, {\left (3 \, B b^{6} d^{7} - 3 \, A a^{6} e^{7} - 3 \, {\left (6 \, B a b^{5} + A b^{6}\right )} d^{6} e + 9 \, {\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} d^{5} e^{2} - 15 \, {\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} d^{4} e^{3} + 15 \, {\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} d^{3} e^{4} - 9 \, {\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} d^{2} e^{5} + 3 \, {\left (B a^{6} + 6 \, A a^{5} b\right )} d e^{6} + 45 \, {\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 )}^{2} - 5 \, {\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 )}\right )}}{{\left (e x + d\right )}^{\frac {5}{2}} e^{7}}\right )}}{315 \, e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.96, size = 675, normalized size = 2.22 \begin {gather*} \frac {{\left (d+e\,x\right )}^{7/2}\,\left (2\,A\,b^6\,e-14\,B\,b^6\,d+12\,B\,a\,b^5\,e\right )}{7\,e^8}-\frac {{\left (d+e\,x\right )}^2\,\left (12\,B\,a^5\,b\,e^5-90\,B\,a^4\,b^2\,d\,e^4+30\,A\,a^4\,b^2\,e^5+240\,B\,a^3\,b^3\,d^2\,e^3-120\,A\,a^3\,b^3\,d\,e^4-300\,B\,a^2\,b^4\,d^3\,e^2+180\,A\,a^2\,b^4\,d^2\,e^3+180\,B\,a\,b^5\,d^4\,e-120\,A\,a\,b^5\,d^3\,e^2-42\,B\,b^6\,d^5+30\,A\,b^6\,d^4\,e\right )+\left (d+e\,x\right )\,\left (\frac {2\,B\,a^6\,e^6}{3}-8\,B\,a^5\,b\,d\,e^5+4\,A\,a^5\,b\,e^6+30\,B\,a^4\,b^2\,d^2\,e^4-20\,A\,a^4\,b^2\,d\,e^5-\frac {160\,B\,a^3\,b^3\,d^3\,e^3}{3}+40\,A\,a^3\,b^3\,d^2\,e^4+50\,B\,a^2\,b^4\,d^4\,e^2-40\,A\,a^2\,b^4\,d^3\,e^3-24\,B\,a\,b^5\,d^5\,e+20\,A\,a\,b^5\,d^4\,e^2+\frac {14\,B\,b^6\,d^6}{3}-4\,A\,b^6\,d^5\,e\right )+\frac {2\,A\,a^6\,e^7}{5}-\frac {2\,B\,b^6\,d^7}{5}+\frac {2\,A\,b^6\,d^6\,e}{5}-\frac {2\,B\,a^6\,d\,e^6}{5}-\frac {12\,A\,a\,b^5\,d^5\,e^2}{5}+\frac {12\,B\,a^5\,b\,d^2\,e^5}{5}+6\,A\,a^2\,b^4\,d^4\,e^3-8\,A\,a^3\,b^3\,d^3\,e^4+6\,A\,a^4\,b^2\,d^2\,e^5-6\,B\,a^2\,b^4\,d^5\,e^2+8\,B\,a^3\,b^3\,d^4\,e^3-6\,B\,a^4\,b^2\,d^3\,e^4-\frac {12\,A\,a^5\,b\,d\,e^6}{5}+\frac {12\,B\,a\,b^5\,d^6\,e}{5}}{e^8\,{\left (d+e\,x\right )}^{5/2}}+\frac {2\,B\,b^6\,{\left (d+e\,x\right )}^{9/2}}{9\,e^8}+\frac {6\,b^4\,\left (a\,e-b\,d\right )\,{\left (d+e\,x\right )}^{5/2}\,\left (2\,A\,b\,e+5\,B\,a\,e-7\,B\,b\,d\right )}{5\,e^8}+\frac {10\,b^2\,{\left (a\,e-b\,d\right )}^3\,\sqrt {d+e\,x}\,\left (4\,A\,b\,e+3\,B\,a\,e-7\,B\,b\,d\right )}{e^8}+\frac {10\,b^3\,{\left (a\,e-b\,d\right )}^2\,{\left (d+e\,x\right )}^{3/2}\,\left (3\,A\,b\,e+4\,B\,a\,e-7\,B\,b\,d\right )}{3\,e^8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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.
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