Optimal. Leaf size=501 \[ -\frac {512 (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{2909907 c^7 e^2 (d+e x)^{7/2}}-\frac {256 (2 c d-b e)^4 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{415701 c^6 e^2 (d+e x)^{5/2}}-\frac {64 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{12597 c^4 e^2 \sqrt {d+e x}}-\frac {4 \sqrt {d+e x} (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{969 c^3 e^2}-\frac {2 (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2} \]
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Rubi [A] time = 0.96, antiderivative size = 501, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {794, 656, 648} \begin {gather*} -\frac {512 (2 c d-b e)^5 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{2909907 c^7 e^2 (d+e x)^{7/2}}-\frac {256 (2 c d-b e)^4 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{415701 c^6 e^2 (d+e x)^{5/2}}-\frac {64 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{12597 c^4 e^2 \sqrt {d+e x}}-\frac {4 \sqrt {d+e x} (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{969 c^3 e^2}-\frac {2 (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-12 b e g+5 c d g+19 c e f)}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 648
Rule 656
Rule 794
Rubi steps
\begin {align*} \int (d+e x)^{5/2} (f+g x) \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2} \, dx &=-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}-\frac {\left (2 \left (\frac {7}{2} e \left (-2 c e^2 f+b e^2 g\right )+\frac {5}{2} \left (-c e^3 f+\left (-c d e^2+b e^3\right ) g\right )\right )\right ) \int (d+e x)^{5/2} \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2} \, dx}{19 c e^3}\\ &=-\frac {2 (19 c e f+5 c d g-12 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}+\frac {(10 (2 c d-b e) (19 c e f+5 c d g-12 b e g)) \int (d+e x)^{3/2} \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2} \, dx}{323 c^2 e}\\ &=-\frac {4 (2 c d-b e) (19 c e f+5 c d g-12 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{969 c^3 e^2}-\frac {2 (19 c e f+5 c d g-12 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}+\frac {\left (16 (2 c d-b e)^2 (19 c e f+5 c d g-12 b e g)\right ) \int \sqrt {d+e x} \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2} \, dx}{969 c^3 e}\\ &=-\frac {32 (2 c d-b e)^2 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12597 c^4 e^2 \sqrt {d+e x}}-\frac {4 (2 c d-b e) (19 c e f+5 c d g-12 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{969 c^3 e^2}-\frac {2 (19 c e f+5 c d g-12 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}+\frac {\left (32 (2 c d-b e)^3 (19 c e f+5 c d g-12 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{\sqrt {d+e x}} \, dx}{4199 c^4 e}\\ &=-\frac {64 (2 c d-b e)^3 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12597 c^4 e^2 \sqrt {d+e x}}-\frac {4 (2 c d-b e) (19 c e f+5 c d g-12 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{969 c^3 e^2}-\frac {2 (19 c e f+5 c d g-12 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}+\frac {\left (128 (2 c d-b e)^4 (19 c e f+5 c d g-12 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^{3/2}} \, dx}{46189 c^5 e}\\ &=-\frac {256 (2 c d-b e)^4 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{415701 c^6 e^2 (d+e x)^{5/2}}-\frac {64 (2 c d-b e)^3 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12597 c^4 e^2 \sqrt {d+e x}}-\frac {4 (2 c d-b e) (19 c e f+5 c d g-12 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{969 c^3 e^2}-\frac {2 (19 c e f+5 c d g-12 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}+\frac {\left (256 (2 c d-b e)^5 (19 c e f+5 c d g-12 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^{5/2}} \, dx}{415701 c^6 e}\\ &=-\frac {512 (2 c d-b e)^5 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{2909907 c^7 e^2 (d+e x)^{7/2}}-\frac {256 (2 c d-b e)^4 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{415701 c^6 e^2 (d+e x)^{5/2}}-\frac {64 (2 c d-b e)^3 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 (19 c e f+5 c d g-12 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12597 c^4 e^2 \sqrt {d+e x}}-\frac {4 (2 c d-b e) (19 c e f+5 c d g-12 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{969 c^3 e^2}-\frac {2 (19 c e f+5 c d g-12 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{323 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{19 c e^2}\\ \end {align*}
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Mathematica [A] time = 0.70, size = 284, normalized size = 0.57 \begin {gather*} \frac {2 ((d+e x) (c (d-e x)-b e))^{7/2} \left (-171171 (b e-c d+c e x)^5 (-6 b e g+11 c d g+c e f)-969969 (2 c d-b e) (b e-c d+c e x)^4 (-3 b e g+5 c d g+c e f)-1322685 (2 c d-b e)^3 (b e-c d+c e x)^2 (-3 b e g+4 c d g+2 c e f)+2238390 (b e-2 c d)^2 (c (d-e x)-b e)^3 (-2 b e g+3 c d g+c e f)+323323 (b e-2 c d)^4 (c (d-e x)-b e) (-6 b e g+7 c d g+5 c e f)-415701 (2 c d-b e)^5 (-b e g+c d g+c e f)-153153 g (b e-c d+c e x)^6\right )}{2909907 c^7 e^2 (d+e x)^{7/2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 4.96, size = 839, normalized size = 1.67 \begin {gather*} -\frac {2 \left ((2 c d-b e) (d+e x)-c (d+e x)^2\right )^{7/2} \left (153153 g (d+e x)^6 c^6+171171 e f (d+e x)^5 c^6+45045 d g (d+e x)^5 c^6+228228 d e f (d+e x)^4 c^6+60060 d^2 g (d+e x)^4 c^6+280896 d^2 e f (d+e x)^3 c^6+73920 d^3 g (d+e x)^3 c^6+306432 d^3 e f (d+e x)^2 c^6+80640 d^4 g (d+e x)^2 c^6+155648 d^5 e f c^6+40960 d^6 g c^6+272384 d^4 e f (d+e x) c^6+71680 d^5 g (d+e x) c^6-108108 b e g (d+e x)^5 c^5-114114 b e^2 f (d+e x)^4 c^5-174174 b d e g (d+e x)^4 c^5-280896 b d e^2 f (d+e x)^3 c^5-251328 b d^2 e g (d+e x)^3 c^5-459648 b d^2 e^2 f (d+e x)^2 c^5-314496 b d^3 e g (d+e x)^2 c^5-389120 b d^4 e^2 f c^5-200704 b d^5 e g c^5-544768 b d^3 e^2 f (d+e x) c^5-315392 b d^4 e g (d+e x) c^5+72072 b^2 e^2 g (d+e x)^4 c^4+70224 b^2 e^3 f (d+e x)^3 c^4+195888 b^2 d e^2 g (d+e x)^3 c^4+229824 b^2 d e^3 f (d+e x)^2 c^4+350784 b^2 d^2 e^2 g (d+e x)^2 c^4+389120 b^2 d^3 e^3 f c^4+348160 b^2 d^4 e^2 g c^4+408576 b^2 d^2 e^3 f (d+e x) c^4+451584 b^2 d^3 e^2 g (d+e x) c^4-44352 b^3 e^3 g (d+e x)^3 c^3-38304 b^3 e^4 f (d+e x)^2 c^3-155232 b^3 d e^3 g (d+e x)^2 c^3-194560 b^3 d^2 e^4 f c^3-296960 b^3 d^3 e^3 g c^3-136192 b^3 d e^4 f (d+e x) c^3-293888 b^3 d^2 e^3 g (d+e x) c^3+24192 b^4 e^4 g (d+e x)^2 c^2+48640 b^4 d e^5 f c^2+135680 b^4 d^2 e^4 g c^2+17024 b^4 e^5 f (d+e x) c^2+90496 b^4 d e^4 g (d+e x) c^2-4864 b^5 e^6 f c-32000 b^5 d e^5 g c-10752 b^5 e^5 g (d+e x) c+3072 b^6 e^6 g\right )}{2909907 c^7 e^2 (d+e x)^{7/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.50, size = 1370, normalized size = 2.73
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int {\left (-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right )}^{\frac {5}{2}} {\left (e x + d\right )}^{\frac {5}{2}} {\left (g x + f\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 739, normalized size = 1.48 \begin {gather*} \frac {2 \left (c e x +b e -c d \right ) \left (153153 g \,e^{6} x^{6} c^{6}-108108 b \,c^{5} e^{6} g \,x^{5}+963963 c^{6} d \,e^{5} g \,x^{5}+171171 c^{6} e^{6} f \,x^{5}+72072 b^{2} c^{4} e^{6} g \,x^{4}-714714 b \,c^{5} d \,e^{5} g \,x^{4}-114114 b \,c^{5} e^{6} f \,x^{4}+2582580 c^{6} d^{2} e^{4} g \,x^{4}+1084083 c^{6} d \,e^{5} f \,x^{4}-44352 b^{3} c^{3} e^{6} g \,x^{3}+484176 b^{2} c^{4} d \,e^{5} g \,x^{3}+70224 b^{2} c^{4} e^{6} f \,x^{3}-2029104 b \,c^{5} d^{2} e^{4} g \,x^{3}-737352 b \,c^{5} d \,e^{5} f \,x^{3}+3827670 c^{6} d^{3} e^{3} g \,x^{3}+2905518 c^{6} d^{2} e^{4} f \,x^{3}+24192 b^{4} c^{2} e^{6} g \,x^{2}-288288 b^{3} c^{3} d \,e^{5} g \,x^{2}-38304 b^{3} c^{3} e^{6} f \,x^{2}+1370880 b^{2} c^{4} d^{2} e^{4} g \,x^{2}+440496 b^{2} c^{4} d \,e^{5} f \,x^{2}-3194604 b \,c^{5} d^{3} e^{3} g \,x^{2}-1987020 b \,c^{5} d^{2} e^{4} f \,x^{2}+3410505 c^{6} d^{4} e^{2} g \,x^{2}+4230198 c^{6} d^{3} e^{3} f \,x^{2}-10752 b^{5} c \,e^{6} g x +138880 b^{4} c^{2} d \,e^{5} g x +17024 b^{4} c^{2} e^{6} f x -737408 b^{3} c^{3} d^{2} e^{4} g x -212800 b^{3} c^{3} d \,e^{5} f x +2029104 b^{2} c^{4} d^{3} e^{3} g x +1078896 b^{2} c^{4} d^{2} e^{4} f x -2935604 b \,c^{5} d^{4} e^{2} g x -2763208 b \,c^{5} d^{3} e^{3} f x +1839103 c^{6} d^{5} e g x +3496703 c^{6} d^{4} e^{2} f x +3072 b^{6} e^{6} g -42752 b^{5} c d \,e^{5} g -4864 b^{5} c \,e^{6} f +250368 b^{4} c^{2} d^{2} e^{4} g +65664 b^{4} c^{2} d \,e^{5} f -790432 b^{3} c^{3} d^{3} e^{3} g -369056 b^{3} c^{3} d^{2} e^{4} f +1418488 b^{2} c^{4} d^{4} e^{2} g +1097744 b^{2} c^{4} d^{3} e^{3} f -1364202 b \,c^{5} d^{5} e g -1788546 b \,c^{5} d^{4} e^{2} f +525458 c^{6} d^{6} g +1414759 f \,d^{5} c^{6} e \right ) \left (-c \,e^{2} x^{2}-b \,e^{2} x -b d e +c \,d^{2}\right )^{\frac {5}{2}}}{2909907 \left (e x +d \right )^{\frac {5}{2}} c^{7} e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.03, size = 1364, normalized size = 2.72
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.39, size = 1307, normalized size = 2.61 \begin {gather*} \frac {\sqrt {c\,d^2-b\,d\,e-c\,e^2\,x^2-b\,e^2\,x}\,\left (\frac {2\,e^4\,x^7\,\sqrt {d+e\,x}\,\left (69\,g\,b^2\,e^2+527\,g\,b\,c\,d\,e+133\,f\,b\,c\,e^2+50\,g\,c^2\,d^2+190\,f\,c^2\,d\,e\right )}{969}+\frac {x^5\,\sqrt {d+e\,x}\,\left (-1512\,g\,b^4\,c^5\,e^9+18018\,g\,b^3\,c^6\,d\,e^8+2394\,f\,b^3\,c^6\,e^9+5734134\,g\,b^2\,c^7\,d^2\,e^7+2882376\,f\,b^2\,c^7\,d\,e^8-527814\,g\,b\,c^8\,d^3\,e^6+5216526\,f\,b\,c^8\,d^2\,e^7-2577456\,g\,c^9\,d^4\,e^5-2810556\,f\,c^9\,d^3\,e^6\right )}{2909907\,c^7\,e^3}+\frac {2\,c^2\,e^6\,g\,x^9\,\sqrt {d+e\,x}}{19}+\frac {x^3\,\sqrt {d+e\,x}\,\left (-1920\,g\,b^6\,c^3\,e^9+26720\,g\,b^5\,c^4\,d\,e^8+3040\,f\,b^5\,c^4\,e^9-156480\,g\,b^4\,c^5\,d^2\,e^7-41040\,f\,b^4\,c^5\,d\,e^8+494020\,g\,b^3\,c^6\,d^3\,e^6+230660\,f\,b^3\,c^6\,d^2\,e^7+3963290\,g\,b^2\,c^7\,d^4\,e^5+9013600\,f\,b^2\,c^7\,d^3\,e^6-7149618\,g\,b\,c^8\,d^5\,e^4-9794310\,f\,b\,c^8\,d^4\,e^5+2823988\,g\,c^9\,d^6\,e^3+1419452\,f\,c^9\,d^5\,e^4\right )}{2909907\,c^7\,e^3}+\frac {x^6\,\sqrt {d+e\,x}\,\left (1386\,g\,b^3\,c^6\,e^9+2409792\,g\,b^2\,c^7\,d\,e^8+482790\,f\,b^2\,c^7\,e^9+4428270\,g\,b\,c^8\,d^2\,e^7+3660426\,f\,b\,c^8\,d\,e^8-2362668\,g\,c^9\,d^3\,e^6+333564\,f\,c^9\,d^2\,e^7\right )}{2909907\,c^7\,e^3}+\frac {2\,c\,e^5\,x^8\,\sqrt {d+e\,x}\,\left (39\,b\,e\,g+56\,c\,d\,g+19\,c\,e\,f\right )}{323}+\frac {2\,{\left (b\,e-c\,d\right )}^3\,\sqrt {d+e\,x}\,\left (3072\,g\,b^6\,e^6-42752\,g\,b^5\,c\,d\,e^5-4864\,f\,b^5\,c\,e^6+250368\,g\,b^4\,c^2\,d^2\,e^4+65664\,f\,b^4\,c^2\,d\,e^5-790432\,g\,b^3\,c^3\,d^3\,e^3-369056\,f\,b^3\,c^3\,d^2\,e^4+1418488\,g\,b^2\,c^4\,d^4\,e^2+1097744\,f\,b^2\,c^4\,d^3\,e^3-1364202\,g\,b\,c^5\,d^5\,e-1788546\,f\,b\,c^5\,d^4\,e^2+525458\,g\,c^6\,d^6+1414759\,f\,c^6\,d^5\,e\right )}{2909907\,c^7\,e^3}+\frac {x^4\,\sqrt {d+e\,x}\,\left (1680\,g\,b^5\,c^4\,e^9-21700\,g\,b^4\,c^5\,d\,e^8-2660\,f\,b^4\,c^5\,e^9+115220\,g\,b^3\,c^6\,d^2\,e^7+33250\,f\,b^3\,c^6\,d\,e^8+6957720\,g\,b^2\,c^7\,d^3\,e^6+7106190\,f\,b^2\,c^7\,d^2\,e^7-7422310\,g\,b\,c^8\,d^4\,e^5-780710\,f\,b\,c^8\,d^3\,e^6+1016036\,g\,c^9\,d^5\,e^4-3122840\,f\,c^9\,d^4\,e^5\right )}{2909907\,c^7\,e^3}+\frac {2\,x^2\,\left (b\,e-c\,d\right )\,\sqrt {d+e\,x}\,\left (384\,g\,b^6\,e^6-5344\,g\,b^5\,c\,d\,e^5-608\,f\,b^5\,c\,e^6+31296\,g\,b^4\,c^2\,d^2\,e^4+8208\,f\,b^4\,c^2\,d\,e^5-98804\,g\,b^3\,c^3\,d^3\,e^3-46132\,f\,b^3\,c^3\,d^2\,e^4+177311\,g\,b^2\,c^4\,d^4\,e^2+137218\,f\,b^2\,c^4\,d^3\,e^3+71967\,g\,b\,c^5\,d^5\,e+988893\,f\,b\,c^5\,d^4\,e^2-176810\,g\,c^6\,d^6-671878\,f\,c^6\,d^5\,e\right )}{969969\,c^5\,e}+\frac {2\,x\,{\left (b\,e-c\,d\right )}^2\,\sqrt {d+e\,x}\,\left (-1536\,g\,b^6\,e^6+21376\,g\,b^5\,c\,d\,e^5+2432\,f\,b^5\,c\,e^6-125184\,g\,b^4\,c^2\,d^2\,e^4-32832\,f\,b^4\,c^2\,d\,e^5+395216\,g\,b^3\,c^3\,d^3\,e^3+184528\,f\,b^3\,c^3\,d^2\,e^4-709244\,g\,b^2\,c^4\,d^4\,e^2-548872\,f\,b^2\,c^4\,d^3\,e^3+682101\,g\,b\,c^5\,d^5\,e+894273\,f\,b\,c^5\,d^4\,e^2-262729\,g\,c^6\,d^6+747574\,f\,c^6\,d^5\,e\right )}{2909907\,c^6\,e^2}\right )}{x+\frac {d}{e}} \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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