Optimal. Leaf size=425 \[ \frac {2 (d+e x)^{7/2} \left (6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right )}{7 e^8}+\frac {6 c^2 (d+e x)^{11/2} \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{11 e^8}-\frac {10 c (d+e x)^{9/2} (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{9 e^8}-\frac {6 (d+e x)^{5/2} (2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{5 e^8}+\frac {2 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{3 e^8}-\frac {2 \sqrt {d+e x} (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{e^8}-\frac {14 c^3 (d+e x)^{13/2} (2 c d-b e)}{13 e^8}+\frac {4 c^4 (d+e x)^{15/2}}{15 e^8} \]
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Rubi [A] time = 0.23, antiderivative size = 425, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {771} \begin {gather*} \frac {2 (d+e x)^{7/2} \left (6 c^2 e^2 \left (a^2 e^2-10 a b d e+15 b^2 d^2\right )-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right )}{7 e^8}+\frac {6 c^2 (d+e x)^{11/2} \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{11 e^8}-\frac {10 c (d+e x)^{9/2} (2 c d-b e) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{9 e^8}-\frac {6 (d+e x)^{5/2} (2 c d-b e) \left (a e^2-b d e+c d^2\right ) \left (-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right )}{5 e^8}+\frac {2 (d+e x)^{3/2} \left (a e^2-b d e+c d^2\right )^2 \left (-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right )}{3 e^8}-\frac {2 \sqrt {d+e x} (2 c d-b e) \left (a e^2-b d e+c d^2\right )^3}{e^8}-\frac {14 c^3 (d+e x)^{13/2} (2 c d-b e)}{13 e^8}+\frac {4 c^4 (d+e x)^{15/2}}{15 e^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 771
Rubi steps
\begin {align*} \int \frac {(b+2 c x) \left (a+b x+c x^2\right )^3}{\sqrt {d+e x}} \, dx &=\int \left (\frac {(-2 c d+b e) \left (c d^2-b d e+a e^2\right )^3}{e^7 \sqrt {d+e x}}+\frac {\left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) \sqrt {d+e x}}{e^7}+\frac {3 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (-7 c^2 d^2+7 b c d e-b^2 e^2-3 a c e^2\right ) (d+e x)^{3/2}}{e^7}+\frac {\left (70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )\right ) (d+e x)^{5/2}}{e^7}+\frac {5 c (2 c d-b e) \left (-7 c^2 d^2-b^2 e^2+c e (7 b d-3 a e)\right ) (d+e x)^{7/2}}{e^7}+\frac {3 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{9/2}}{e^7}-\frac {7 c^3 (2 c d-b e) (d+e x)^{11/2}}{e^7}+\frac {2 c^4 (d+e x)^{13/2}}{e^7}\right ) \, dx\\ &=-\frac {2 (2 c d-b e) \left (c d^2-b d e+a e^2\right )^3 \sqrt {d+e x}}{e^8}+\frac {2 \left (c d^2-b d e+a e^2\right )^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{3/2}}{3 e^8}-\frac {6 (2 c d-b e) \left (c d^2-b d e+a e^2\right ) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right ) (d+e x)^{5/2}}{5 e^8}+\frac {2 \left (70 c^4 d^4+b^4 e^4-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+6 c^2 e^2 \left (15 b^2 d^2-10 a b d e+a^2 e^2\right )\right ) (d+e x)^{7/2}}{7 e^8}-\frac {10 c (2 c d-b e) \left (7 c^2 d^2+b^2 e^2-c e (7 b d-3 a e)\right ) (d+e x)^{9/2}}{9 e^8}+\frac {6 c^2 \left (14 c^2 d^2+3 b^2 e^2-2 c e (7 b d-a e)\right ) (d+e x)^{11/2}}{11 e^8}-\frac {14 c^3 (2 c d-b e) (d+e x)^{13/2}}{13 e^8}+\frac {4 c^4 (d+e x)^{15/2}}{15 e^8}\\ \end {align*}
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Mathematica [A] time = 0.62, size = 599, normalized size = 1.41 \begin {gather*} \frac {2 \sqrt {d+e x} \left (-39 c^2 e^2 \left (198 a^2 e^2 \left (16 d^3-8 d^2 e x+6 d e^2 x^2-5 e^3 x^3\right )-55 a b e \left (128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right )+15 b^2 \left (256 d^5-128 d^4 e x+96 d^3 e^2 x^2-80 d^2 e^3 x^3+70 d e^4 x^4-63 e^5 x^5\right )\right )+143 c e^3 \left (210 a^3 e^3 (e x-2 d)+189 a^2 b e^2 \left (8 d^2-4 d e x+3 e^2 x^2\right )+108 a b^2 e \left (-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right )+5 b^3 \left (128 d^4-64 d^3 e x+48 d^2 e^2 x^2-40 d e^3 x^3+35 e^4 x^4\right )\right )+1287 b e^4 \left (35 a^3 e^3+35 a^2 b e^2 (e x-2 d)+7 a b^2 e \left (8 d^2-4 d e x+3 e^2 x^2\right )+b^3 \left (-16 d^3+8 d^2 e x-6 d e^2 x^2+5 e^3 x^3\right )\right )+15 c^3 e \left (26 a e \left (-256 d^5+128 d^4 e x-96 d^3 e^2 x^2+80 d^2 e^3 x^3-70 d e^4 x^4+63 e^5 x^5\right )+7 b \left (1024 d^6-512 d^5 e x+384 d^4 e^2 x^2-320 d^3 e^3 x^3+280 d^2 e^4 x^4-252 d e^5 x^5+231 e^6 x^6\right )\right )-14 c^4 \left (2048 d^7-1024 d^6 e x+768 d^5 e^2 x^2-640 d^4 e^3 x^3+560 d^3 e^4 x^4-504 d^2 e^5 x^5+462 d e^6 x^6-429 e^7 x^7\right )\right )}{45045 e^8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [B] time = 0.37, size = 1186, normalized size = 2.79 \begin {gather*} -\frac {2 \left (-6006 c^4 (d+e x)^{15/2}+48510 c^4 d (d+e x)^{13/2}-24255 b c^3 e (d+e x)^{13/2}-171990 c^4 d^2 (d+e x)^{11/2}-24570 a c^3 e^2 (d+e x)^{11/2}-36855 b^2 c^2 e^2 (d+e x)^{11/2}+171990 b c^3 d e (d+e x)^{11/2}+350350 c^4 d^3 (d+e x)^{9/2}-75075 a b c^2 e^3 (d+e x)^{9/2}-25025 b^3 c e^3 (d+e x)^{9/2}+150150 a c^3 d e^2 (d+e x)^{9/2}+225225 b^2 c^2 d e^2 (d+e x)^{9/2}-525525 b c^3 d^2 e (d+e x)^{9/2}-450450 c^4 d^4 (d+e x)^{7/2}-6435 b^4 e^4 (d+e x)^{7/2}-38610 a^2 c^2 e^4 (d+e x)^{7/2}-77220 a b^2 c e^4 (d+e x)^{7/2}+386100 a b c^2 d e^3 (d+e x)^{7/2}+128700 b^3 c d e^3 (d+e x)^{7/2}-386100 a c^3 d^2 e^2 (d+e x)^{7/2}-579150 b^2 c^2 d^2 e^2 (d+e x)^{7/2}+900900 b c^3 d^3 e (d+e x)^{7/2}+378378 c^4 d^5 (d+e x)^{5/2}-27027 a b^3 e^5 (d+e x)^{5/2}-81081 a^2 b c e^5 (d+e x)^{5/2}+27027 b^4 d e^4 (d+e x)^{5/2}+162162 a^2 c^2 d e^4 (d+e x)^{5/2}+324324 a b^2 c d e^4 (d+e x)^{5/2}-810810 a b c^2 d^2 e^3 (d+e x)^{5/2}-270270 b^3 c d^2 e^3 (d+e x)^{5/2}+540540 a c^3 d^3 e^2 (d+e x)^{5/2}+810810 b^2 c^2 d^3 e^2 (d+e x)^{5/2}-945945 b c^3 d^4 e (d+e x)^{5/2}-210210 c^4 d^6 (d+e x)^{3/2}-45045 a^2 b^2 e^6 (d+e x)^{3/2}-30030 a^3 c e^6 (d+e x)^{3/2}+90090 a b^3 d e^5 (d+e x)^{3/2}+270270 a^2 b c d e^5 (d+e x)^{3/2}-45045 b^4 d^2 e^4 (d+e x)^{3/2}-270270 a^2 c^2 d^2 e^4 (d+e x)^{3/2}-540540 a b^2 c d^2 e^4 (d+e x)^{3/2}+900900 a b c^2 d^3 e^3 (d+e x)^{3/2}+300300 b^3 c d^3 e^3 (d+e x)^{3/2}-450450 a c^3 d^4 e^2 (d+e x)^{3/2}-675675 b^2 c^2 d^4 e^2 (d+e x)^{3/2}+630630 b c^3 d^5 e (d+e x)^{3/2}+90090 c^4 d^7 \sqrt {d+e x}-45045 a^3 b e^7 \sqrt {d+e x}+135135 a^2 b^2 d e^6 \sqrt {d+e x}+90090 a^3 c d e^6 \sqrt {d+e x}-135135 a b^3 d^2 e^5 \sqrt {d+e x}-405405 a^2 b c d^2 e^5 \sqrt {d+e x}+45045 b^4 d^3 e^4 \sqrt {d+e x}+270270 a^2 c^2 d^3 e^4 \sqrt {d+e x}+540540 a b^2 c d^3 e^4 \sqrt {d+e x}-675675 a b c^2 d^4 e^3 \sqrt {d+e x}-225225 b^3 c d^4 e^3 \sqrt {d+e x}+270270 a c^3 d^5 e^2 \sqrt {d+e x}+405405 b^2 c^2 d^5 e^2 \sqrt {d+e x}-315315 b c^3 d^6 e \sqrt {d+e x}\right )}{45045 e^8} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 648, normalized size = 1.52 \begin {gather*} \frac {2 \, {\left (6006 \, c^{4} e^{7} x^{7} - 28672 \, c^{4} d^{7} + 107520 \, b c^{3} d^{6} e + 45045 \, a^{3} b e^{7} - 49920 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{5} e^{2} + 91520 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{4} e^{3} - 20592 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{3} e^{4} + 72072 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{2} e^{5} - 30030 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d e^{6} - 1617 \, {\left (4 \, c^{4} d e^{6} - 15 \, b c^{3} e^{7}\right )} x^{6} + 63 \, {\left (112 \, c^{4} d^{2} e^{5} - 420 \, b c^{3} d e^{6} + 195 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} e^{7}\right )} x^{5} - 35 \, {\left (224 \, c^{4} d^{3} e^{4} - 840 \, b c^{3} d^{2} e^{5} + 390 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d e^{6} - 715 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} e^{7}\right )} x^{4} + 5 \, {\left (1792 \, c^{4} d^{4} e^{3} - 6720 \, b c^{3} d^{3} e^{4} + 3120 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{2} e^{5} - 5720 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d e^{6} + 1287 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} e^{7}\right )} x^{3} - 3 \, {\left (3584 \, c^{4} d^{5} e^{2} - 13440 \, b c^{3} d^{4} e^{3} + 6240 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{3} e^{4} - 11440 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{2} e^{5} + 2574 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d e^{6} - 9009 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} e^{7}\right )} x^{2} + {\left (14336 \, c^{4} d^{6} e - 53760 \, b c^{3} d^{5} e^{2} + 24960 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{4} e^{3} - 45760 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{3} e^{4} + 10296 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{2} e^{5} - 36036 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d e^{6} + 15015 \, {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} e^{7}\right )} x\right )} \sqrt {e x + d}}{45045 \, e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.23, size = 841, normalized size = 1.98
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 = 795, normalized size = 1.87 \begin {gather*} \frac {2 \sqrt {e x +d}\, \left (6006 c^{4} e^{7} x^{7}+24255 b \,c^{3} e^{7} x^{6}-6468 c^{4} d \,e^{6} x^{6}+24570 a \,c^{3} e^{7} x^{5}+36855 b^{2} c^{2} e^{7} x^{5}-26460 b \,c^{3} d \,e^{6} x^{5}+7056 c^{4} d^{2} e^{5} x^{5}+75075 a b \,c^{2} e^{7} x^{4}-27300 a \,c^{3} d \,e^{6} x^{4}+25025 b^{3} c \,e^{7} x^{4}-40950 b^{2} c^{2} d \,e^{6} x^{4}+29400 b \,c^{3} d^{2} e^{5} x^{4}-7840 c^{4} d^{3} e^{4} x^{4}+38610 a^{2} c^{2} e^{7} x^{3}+77220 a \,b^{2} c \,e^{7} x^{3}-85800 a b \,c^{2} d \,e^{6} x^{3}+31200 a \,c^{3} d^{2} e^{5} x^{3}+6435 b^{4} e^{7} x^{3}-28600 b^{3} c d \,e^{6} x^{3}+46800 b^{2} c^{2} d^{2} e^{5} x^{3}-33600 b \,c^{3} d^{3} e^{4} x^{3}+8960 c^{4} d^{4} e^{3} x^{3}+81081 a^{2} b c \,e^{7} x^{2}-46332 a^{2} c^{2} d \,e^{6} x^{2}+27027 a \,b^{3} e^{7} x^{2}-92664 a \,b^{2} c d \,e^{6} x^{2}+102960 a b \,c^{2} d^{2} e^{5} x^{2}-37440 a \,c^{3} d^{3} e^{4} x^{2}-7722 b^{4} d \,e^{6} x^{2}+34320 b^{3} c \,d^{2} e^{5} x^{2}-56160 b^{2} c^{2} d^{3} e^{4} x^{2}+40320 b \,c^{3} d^{4} e^{3} x^{2}-10752 c^{4} d^{5} e^{2} x^{2}+30030 a^{3} c \,e^{7} x +45045 a^{2} b^{2} e^{7} x -108108 a^{2} b c d \,e^{6} x +61776 a^{2} c^{2} d^{2} e^{5} x -36036 a \,b^{3} d \,e^{6} x +123552 a \,b^{2} c \,d^{2} e^{5} x -137280 a b \,c^{2} d^{3} e^{4} x +49920 a \,c^{3} d^{4} e^{3} x +10296 b^{4} d^{2} e^{5} x -45760 b^{3} c \,d^{3} e^{4} x +74880 b^{2} c^{2} d^{4} e^{3} x -53760 b \,c^{3} d^{5} e^{2} x +14336 c^{4} d^{6} e x +45045 b \,a^{3} e^{7}-60060 a^{3} c d \,e^{6}-90090 a^{2} b^{2} d \,e^{6}+216216 a^{2} b c \,d^{2} e^{5}-123552 a^{2} c^{2} d^{3} e^{4}+72072 a \,b^{3} d^{2} e^{5}-247104 a \,b^{2} c \,d^{3} e^{4}+274560 a b \,c^{2} d^{4} e^{3}-99840 a \,c^{3} d^{5} e^{2}-20592 b^{4} d^{3} e^{4}+91520 b^{3} c \,d^{4} e^{3}-149760 b^{2} c^{2} d^{5} e^{2}+107520 b \,c^{3} d^{6} e -28672 c^{4} d^{7}\right )}{45045 e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 645, normalized size = 1.52 \begin {gather*} \frac {2 \, {\left (6006 \, {\left (e x + d\right )}^{\frac {15}{2}} c^{4} - 24255 \, {\left (2 \, c^{4} d - b c^{3} e\right )} {\left (e x + d\right )}^{\frac {13}{2}} + 12285 \, {\left (14 \, c^{4} d^{2} - 14 \, b c^{3} d e + {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} e^{2}\right )} {\left (e x + d\right )}^{\frac {11}{2}} - 25025 \, {\left (14 \, c^{4} d^{3} - 21 \, b c^{3} d^{2} e + 3 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d e^{2} - {\left (b^{3} c + 3 \, a b c^{2}\right )} e^{3}\right )} {\left (e x + d\right )}^{\frac {9}{2}} + 6435 \, {\left (70 \, c^{4} d^{4} - 140 \, b c^{3} d^{3} e + 30 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{2} e^{2} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d e^{3} + {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} e^{4}\right )} {\left (e x + d\right )}^{\frac {7}{2}} - 27027 \, {\left (14 \, c^{4} d^{5} - 35 \, b c^{3} d^{4} e + 10 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{3} e^{2} - 10 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{2} e^{3} + {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d e^{4} - {\left (a b^{3} + 3 \, a^{2} b c\right )} e^{5}\right )} {\left (e x + d\right )}^{\frac {5}{2}} + 15015 \, {\left (14 \, c^{4} d^{6} - 42 \, b c^{3} d^{5} e + 15 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{4} e^{2} - 20 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{3} e^{3} + 3 \, {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{2} e^{4} - 6 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d e^{5} + {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} e^{6}\right )} {\left (e x + d\right )}^{\frac {3}{2}} - 45045 \, {\left (2 \, c^{4} d^{7} - 7 \, b c^{3} d^{6} e - a^{3} b e^{7} + 3 \, {\left (3 \, b^{2} c^{2} + 2 \, a c^{3}\right )} d^{5} e^{2} - 5 \, {\left (b^{3} c + 3 \, a b c^{2}\right )} d^{4} e^{3} + {\left (b^{4} + 12 \, a b^{2} c + 6 \, a^{2} c^{2}\right )} d^{3} e^{4} - 3 \, {\left (a b^{3} + 3 \, a^{2} b c\right )} d^{2} e^{5} + {\left (3 \, a^{2} b^{2} + 2 \, a^{3} c\right )} d e^{6}\right )} \sqrt {e x + d}\right )}}{45045 \, e^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.93, size = 444, normalized size = 1.04 \begin {gather*} \frac {{\left (d+e\,x\right )}^{11/2}\,\left (18\,b^2\,c^2\,e^2-84\,b\,c^3\,d\,e+84\,c^4\,d^2+12\,a\,c^3\,e^2\right )}{11\,e^8}+\frac {4\,c^4\,{\left (d+e\,x\right )}^{15/2}}{15\,e^8}-\frac {\left (28\,c^4\,d-14\,b\,c^3\,e\right )\,{\left (d+e\,x\right )}^{13/2}}{13\,e^8}+\frac {{\left (d+e\,x\right )}^{7/2}\,\left (12\,a^2\,c^2\,e^4+24\,a\,b^2\,c\,e^4-120\,a\,b\,c^2\,d\,e^3+120\,a\,c^3\,d^2\,e^2+2\,b^4\,e^4-40\,b^3\,c\,d\,e^3+180\,b^2\,c^2\,d^2\,e^2-280\,b\,c^3\,d^3\,e+140\,c^4\,d^4\right )}{7\,e^8}+\frac {2\,\left (b\,e-2\,c\,d\right )\,\sqrt {d+e\,x}\,{\left (c\,d^2-b\,d\,e+a\,e^2\right )}^3}{e^8}+\frac {6\,\left (b\,e-2\,c\,d\right )\,{\left (d+e\,x\right )}^{5/2}\,\left (3\,a^2\,c\,e^4+a\,b^2\,e^4-10\,a\,b\,c\,d\,e^3+10\,a\,c^2\,d^2\,e^2-b^3\,d\,e^3+8\,b^2\,c\,d^2\,e^2-14\,b\,c^2\,d^3\,e+7\,c^3\,d^4\right )}{5\,e^8}+\frac {2\,{\left (d+e\,x\right )}^{3/2}\,{\left (c\,d^2-b\,d\,e+a\,e^2\right )}^2\,\left (3\,b^2\,e^2-14\,b\,c\,d\,e+14\,c^2\,d^2+2\,a\,c\,e^2\right )}{3\,e^8}+\frac {10\,c\,\left (b\,e-2\,c\,d\right )\,{\left (d+e\,x\right )}^{9/2}\,\left (b^2\,e^2-7\,b\,c\,d\,e+7\,c^2\,d^2+3\,a\,c\,e^2\right )}{9\,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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