Optimal. Leaf size=424 \[ -\frac {256 (2 c d-b e)^4 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{765765 c^6 e^2 (d+e x)^{7/2}}-\frac {128 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{109395 c^5 e^2 (d+e x)^{5/2}}-\frac {32 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac {16 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{3315 c^3 e^2 \sqrt {d+e x}}-\frac {2 \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2} \]
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Rubi [A] time = 0.76, antiderivative size = 424, normalized size of antiderivative = 1.00, number of steps used = 6, 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 {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} (-10 b e g+3 c d g+17 c e f)}{765765 c^6 e^2 (d+e x)^{7/2}}-\frac {128 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{109395 c^5 e^2 (d+e x)^{5/2}}-\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} (-10 b e g+3 c d g+17 c e f)}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac {16 (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{3315 c^3 e^2 \sqrt {d+e x}}-\frac {2 \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2} (-10 b e g+3 c d g+17 c e f)}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 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)^{3/2} (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)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2}-\frac {\left (2 \left (\frac {7}{2} e \left (-2 c e^2 f+b e^2 g\right )+\frac {3}{2} \left (-c e^3 f+\left (-c d e^2+b e^3\right ) g\right )\right )\right ) \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}{17 c e^3}\\ &=-\frac {2 (17 c e f+3 c d g-10 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}}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2}+\frac {(8 (2 c d-b e) (17 c e f+3 c d g-10 b e g)) \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}{255 c^2 e}\\ &=-\frac {16 (2 c d-b e) (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{3315 c^3 e^2 \sqrt {d+e x}}-\frac {2 (17 c e f+3 c d g-10 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}}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2}+\frac {\left (16 (2 c d-b e)^2 (17 c e f+3 c d g-10 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}{1105 c^3 e}\\ &=-\frac {32 (2 c d-b e)^2 (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac {16 (2 c d-b e) (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{3315 c^3 e^2 \sqrt {d+e x}}-\frac {2 (17 c e f+3 c d g-10 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}}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2}+\frac {\left (64 (2 c d-b e)^3 (17 c e f+3 c d g-10 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}{12155 c^4 e}\\ &=-\frac {128 (2 c d-b e)^3 (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{109395 c^5 e^2 (d+e x)^{5/2}}-\frac {32 (2 c d-b e)^2 (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac {16 (2 c d-b e) (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{3315 c^3 e^2 \sqrt {d+e x}}-\frac {2 (17 c e f+3 c d g-10 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}}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2}+\frac {\left (128 (2 c d-b e)^4 (17 c e f+3 c d g-10 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}{109395 c^5 e}\\ &=-\frac {256 (2 c d-b e)^4 (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{765765 c^6 e^2 (d+e x)^{7/2}}-\frac {128 (2 c d-b e)^3 (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{109395 c^5 e^2 (d+e x)^{5/2}}-\frac {32 (2 c d-b e)^2 (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac {16 (2 c d-b e) (17 c e f+3 c d g-10 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{3315 c^3 e^2 \sqrt {d+e x}}-\frac {2 (17 c e f+3 c d g-10 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}}{255 c^2 e^2}-\frac {2 g (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{17 c e^2}\\ \end {align*}
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Mathematica [A] time = 0.38, size = 367, normalized size = 0.87 \begin {gather*} \frac {2 (b e-c d+c e x)^3 \sqrt {(d+e x) (c (d-e x)-b e)} \left (-1280 b^5 e^5 g+128 b^4 c e^4 (118 d g+17 e f+35 e g x)-32 b^3 c^2 e^3 \left (2253 d^2 g+2 d e (391 f+756 g x)+7 e^2 x (34 f+45 g x)\right )+16 b^2 c^3 e^2 \left (10864 d^3 g+3 d^2 e (2397 f+4249 g x)+294 d e^2 x (17 f+21 g x)+21 e^3 x^2 (51 f+55 g x)\right )-2 b c^4 e \left (104843 d^4 g+4 d^3 e (32623 f+50554 g x)+42 d^2 e^2 x (3842 f+4287 g x)+84 d e^3 x^2 (969 f+968 g x)+231 e^4 x^3 (68 f+65 g x)\right )+c^5 \left (94134 d^5 g+d^4 e (278171 f+329469 g x)+28 d^3 e^2 x (21097 f+19638 g x)+126 d^2 e^3 x^2 (4471 f+3949 g x)+462 d e^4 x^3 (578 f+507 g x)+3003 e^5 x^4 (17 f+15 g x)\right )\right )}{765765 c^6 e^2 \sqrt {d+e x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 4.44, size = 598, normalized size = 1.41 \begin {gather*} -\frac {2 \left ((d+e x) (2 c d-b e)-c (d+e x)^2\right )^{7/2} \left (-1280 b^5 e^5 g+4480 b^4 c e^4 g (d+e x)+10624 b^4 c d e^4 g+2176 b^4 c e^5 f-33792 b^3 c^2 d^2 e^3 g-7616 b^3 c^2 e^4 f (d+e x)-17408 b^3 c^2 d e^4 f-10080 b^3 c^2 e^3 g (d+e x)^2-28224 b^3 c^2 d e^3 g (d+e x)+50176 b^2 c^3 d^3 e^2 g+52224 b^2 c^3 d^2 e^3 f+61824 b^2 c^3 d^2 e^2 g (d+e x)+17136 b^2 c^3 e^3 f (d+e x)^2+45696 b^2 c^3 d e^3 f (d+e x)+18480 b^2 c^3 e^2 g (d+e x)^3+43344 b^2 c^3 d e^2 g (d+e x)^2-32768 b c^4 d^4 e g-69632 b c^4 d^3 e^2 f-51968 b c^4 d^3 e g (d+e x)-91392 b c^4 d^2 e^2 f (d+e x)-52416 b c^4 d^2 e g (d+e x)^2-31416 b c^4 e^2 f (d+e x)^3-68544 b c^4 d e^2 f (d+e x)^2-30030 b c^4 e g (d+e x)^4-42504 b c^4 d e g (d+e x)^3+6144 c^5 d^5 g+34816 c^5 d^4 e f+10752 c^5 d^4 g (d+e x)+60928 c^5 d^3 e f (d+e x)+12096 c^5 d^3 g (d+e x)^2+68544 c^5 d^2 e f (d+e x)^2+11088 c^5 d^2 g (d+e x)^3+51051 c^5 e f (d+e x)^4+62832 c^5 d e f (d+e x)^3+45045 c^5 g (d+e x)^5+9009 c^5 d g (d+e x)^4\right )}{765765 c^6 e^2 (d+e x)^{7/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.47, size = 1112, normalized size = 2.62
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 {3}{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 = 535, normalized size = 1.26 \begin {gather*} -\frac {2 \left (c e x +b e -c d \right ) \left (-45045 g \,e^{5} x^{5} c^{5}+30030 b \,c^{4} e^{5} g \,x^{4}-234234 c^{5} d \,e^{4} g \,x^{4}-51051 c^{5} e^{5} f \,x^{4}-18480 b^{2} c^{3} e^{5} g \,x^{3}+162624 b \,c^{4} d \,e^{4} g \,x^{3}+31416 b \,c^{4} e^{5} f \,x^{3}-497574 c^{5} d^{2} e^{3} g \,x^{3}-267036 c^{5} d \,e^{4} f \,x^{3}+10080 b^{3} c^{2} e^{5} g \,x^{2}-98784 b^{2} c^{3} d \,e^{4} g \,x^{2}-17136 b^{2} c^{3} e^{5} f \,x^{2}+360108 b \,c^{4} d^{2} e^{3} g \,x^{2}+162792 b \,c^{4} d \,e^{4} f \,x^{2}-549864 c^{5} d^{3} e^{2} g \,x^{2}-563346 c^{5} d^{2} e^{3} f \,x^{2}-4480 b^{4} c \,e^{5} g x +48384 b^{3} c^{2} d \,e^{4} g x +7616 b^{3} c^{2} e^{5} f x -203952 b^{2} c^{3} d^{2} e^{3} g x -79968 b^{2} c^{3} d \,e^{4} f x +404432 b \,c^{4} d^{3} e^{2} g x +322728 b \,c^{4} d^{2} e^{3} f x -329469 c^{5} d^{4} e g x -590716 c^{5} d^{3} e^{2} f x +1280 b^{5} e^{5} g -15104 b^{4} c d \,e^{4} g -2176 b^{4} c \,e^{5} f +72096 b^{3} c^{2} d^{2} e^{3} g +25024 b^{3} c^{2} d \,e^{4} f -173824 b^{2} c^{3} d^{3} e^{2} g -115056 b^{2} c^{3} d^{2} e^{3} f +209686 b \,c^{4} d^{4} e g +260984 b \,c^{4} d^{3} e^{2} f -94134 c^{5} d^{5} g -278171 f \,d^{4} c^{5} e \right ) \left (-c \,e^{2} x^{2}-b \,e^{2} x -b d e +c \,d^{2}\right )^{\frac {5}{2}}}{765765 \left (e x +d \right )^{\frac {5}{2}} c^{6} e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.03, size = 1108, normalized size = 2.61 \begin {gather*} \frac {2 \, {\left (3003 \, c^{7} e^{7} x^{7} - 16363 \, c^{7} d^{7} + 64441 \, b c^{6} d^{6} e - 101913 \, b^{2} c^{5} d^{5} e^{2} + 84195 \, b^{3} c^{4} d^{4} e^{3} - 40200 \, b^{4} c^{3} d^{3} e^{4} + 11568 \, b^{5} c^{2} d^{2} e^{5} - 1856 \, b^{6} c d e^{6} + 128 \, b^{7} e^{7} + 231 \, {\left (29 \, c^{7} d e^{6} + 31 \, b c^{6} e^{7}\right )} x^{6} - 63 \, {\left (79 \, c^{7} d^{2} e^{5} - 398 \, b c^{6} d e^{6} - 71 \, b^{2} c^{5} e^{7}\right )} x^{5} - 35 \, {\left (587 \, c^{7} d^{3} e^{4} - 525 \, b c^{6} d^{2} e^{5} - 633 \, b^{2} c^{5} d e^{6} - b^{3} c^{4} e^{7}\right )} x^{4} - 5 \, {\left (835 \, c^{7} d^{4} e^{3} + 6548 \, b c^{6} d^{3} e^{4} - 8586 \, b^{2} c^{5} d^{2} e^{5} - 92 \, b^{3} c^{4} d e^{6} + 8 \, b^{4} c^{3} e^{7}\right )} x^{3} + 3 \, {\left (7339 \, c^{7} d^{5} e^{2} - 20435 \, b c^{6} d^{4} e^{3} + 12250 \, b^{2} c^{5} d^{3} e^{4} + 1030 \, b^{3} c^{4} d^{2} e^{5} - 200 \, b^{4} c^{3} d e^{6} + 16 \, b^{5} c^{2} e^{7}\right )} x^{2} + {\left (14341 \, c^{7} d^{6} e - 21006 \, b c^{6} d^{5} e^{2} - 4395 \, b^{2} c^{5} d^{4} e^{3} + 15180 \, b^{3} c^{4} d^{3} e^{4} - 4920 \, b^{4} c^{3} d^{2} e^{5} + 864 \, b^{5} c^{2} d e^{6} - 64 \, b^{6} c e^{7}\right )} x\right )} \sqrt {-c e x + c d - b e} {\left (e x + d\right )} f}{45045 \, {\left (c^{5} e^{2} x + c^{5} d e\right )}} + \frac {2 \, {\left (45045 \, c^{8} e^{8} x^{8} - 94134 \, c^{8} d^{8} + 492088 \, b c^{7} d^{7} e - 1085284 \, b^{2} c^{6} d^{6} e^{2} + 1316760 \, b^{3} c^{5} d^{5} e^{3} - 962550 \, b^{4} c^{4} d^{4} e^{4} + 436704 \, b^{5} c^{3} d^{3} e^{5} - 121248 \, b^{6} c^{2} d^{2} e^{6} + 18944 \, b^{7} c d e^{7} - 1280 \, b^{8} e^{8} + 3003 \, {\left (33 \, c^{8} d e^{7} + 35 \, b c^{7} e^{8}\right )} x^{7} - 231 \, {\left (303 \, c^{8} d^{2} e^{6} - 1558 \, b c^{7} d e^{7} - 275 \, b^{2} c^{6} e^{8}\right )} x^{6} - 63 \, {\left (4527 \, c^{8} d^{3} e^{5} - 4129 \, b c^{7} d^{2} e^{6} - 4813 \, b^{2} c^{6} d e^{7} - 5 \, b^{3} c^{5} e^{8}\right )} x^{5} - 35 \, {\left (1761 \, c^{8} d^{4} e^{4} + 11860 \, b c^{7} d^{3} e^{5} - 15954 \, b^{2} c^{6} d^{2} e^{6} - 108 \, b^{3} c^{5} d e^{7} + 10 \, b^{4} c^{4} e^{8}\right )} x^{4} + 5 \, {\left (51549 \, c^{8} d^{5} e^{3} - 146429 \, b c^{7} d^{4} e^{4} + 91238 \, b^{2} c^{6} d^{3} e^{5} + 4506 \, b^{3} c^{5} d^{2} e^{6} - 944 \, b^{4} c^{4} d e^{7} + 80 \, b^{5} c^{3} e^{8}\right )} x^{3} + 3 \, {\left (52047 \, c^{8} d^{6} e^{2} - 89650 \, b c^{7} d^{5} e^{3} + 15875 \, b^{2} c^{6} d^{4} e^{4} + 30740 \, b^{3} c^{5} d^{3} e^{5} - 10900 \, b^{4} c^{4} d^{2} e^{6} + 2048 \, b^{5} c^{3} d e^{7} - 160 \, b^{6} c^{2} e^{8}\right )} x^{2} - {\left (47067 \, c^{8} d^{7} e - 198977 \, b c^{7} d^{6} e^{2} + 343665 \, b^{2} c^{6} d^{5} e^{3} - 314715 \, b^{3} c^{5} d^{4} e^{4} + 166560 \, b^{4} c^{4} d^{3} e^{5} - 51792 \, b^{5} c^{3} d^{2} e^{6} + 8832 \, b^{6} c^{2} d e^{7} - 640 \, b^{7} c e^{8}\right )} x\right )} \sqrt {-c e x + c d - b e} {\left (e x + d\right )} g}{765765 \, {\left (c^{6} e^{3} x + c^{6} d e^{2}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.64, size = 1023, normalized size = 2.41 \begin {gather*} \frac {\sqrt {c\,d^2-b\,d\,e-c\,e^2\,x^2-b\,e^2\,x}\,\left (\frac {2\,e^3\,x^6\,\sqrt {d+e\,x}\,\left (275\,g\,b^2\,e^2+1558\,g\,b\,c\,d\,e+527\,f\,b\,c\,e^2-303\,g\,c^2\,d^2+493\,f\,c^2\,d\,e\right )}{3315}+\frac {2\,{\left (b\,e-c\,d\right )}^3\,\sqrt {d+e\,x}\,\left (-1280\,g\,b^5\,e^5+15104\,g\,b^4\,c\,d\,e^4+2176\,f\,b^4\,c\,e^5-72096\,g\,b^3\,c^2\,d^2\,e^3-25024\,f\,b^3\,c^2\,d\,e^4+173824\,g\,b^2\,c^3\,d^3\,e^2+115056\,f\,b^2\,c^3\,d^2\,e^3-209686\,g\,b\,c^4\,d^4\,e-260984\,f\,b\,c^4\,d^3\,e^2+94134\,g\,c^5\,d^5+278171\,f\,c^5\,d^4\,e\right )}{765765\,c^6\,e^3}+\frac {x^4\,\sqrt {d+e\,x}\,\left (-700\,g\,b^4\,c^4\,e^8+7560\,g\,b^3\,c^5\,d\,e^7+1190\,f\,b^3\,c^5\,e^8+1116780\,g\,b^2\,c^6\,d^2\,e^6+753270\,f\,b^2\,c^6\,d\,e^7-830200\,g\,b\,c^7\,d^3\,e^5+624750\,f\,b\,c^7\,d^2\,e^6-123270\,g\,c^8\,d^4\,e^4-698530\,f\,c^8\,d^3\,e^5\right )}{765765\,c^6\,e^3}+\frac {2\,c^2\,e^5\,g\,x^8\,\sqrt {d+e\,x}}{17}+\frac {x^5\,\sqrt {d+e\,x}\,\left (630\,g\,b^3\,c^5\,e^8+606438\,g\,b^2\,c^6\,d\,e^7+152082\,f\,b^2\,c^6\,e^8+520254\,g\,b\,c^7\,d^2\,e^6+852516\,f\,b\,c^7\,d\,e^7-570402\,g\,c^8\,d^3\,e^5-169218\,f\,c^8\,d^2\,e^6\right )}{765765\,c^6\,e^3}+\frac {2\,c\,e^4\,x^7\,\sqrt {d+e\,x}\,\left (35\,b\,e\,g+33\,c\,d\,g+17\,c\,e\,f\right )}{255}+\frac {x^3\,\sqrt {d+e\,x}\,\left (800\,g\,b^5\,c^3\,e^8-9440\,g\,b^4\,c^4\,d\,e^7-1360\,f\,b^4\,c^4\,e^8+45060\,g\,b^3\,c^5\,d^2\,e^6+15640\,f\,b^3\,c^5\,d\,e^7+912380\,g\,b^2\,c^6\,d^3\,e^5+1459620\,f\,b^2\,c^6\,d^2\,e^6-1464290\,g\,b\,c^7\,d^4\,e^4-1113160\,f\,b\,c^7\,d^3\,e^5+515490\,g\,c^8\,d^5\,e^3-141950\,f\,c^8\,d^4\,e^4\right )}{765765\,c^6\,e^3}+\frac {2\,x^2\,\left (b\,e-c\,d\right )\,\sqrt {d+e\,x}\,\left (-160\,g\,b^5\,e^5+1888\,g\,b^4\,c\,d\,e^4+272\,f\,b^4\,c\,e^5-9012\,g\,b^3\,c^2\,d^2\,e^3-3128\,f\,b^3\,c^2\,d\,e^4+21728\,g\,b^2\,c^3\,d^3\,e^2+14382\,f\,b^2\,c^3\,d^2\,e^3+37603\,g\,b\,c^4\,d^4\,e+222632\,f\,b\,c^4\,d^3\,e^2-52047\,g\,c^5\,d^5-124763\,f\,c^5\,d^4\,e\right )}{255255\,c^4\,e}+\frac {2\,x\,{\left (b\,e-c\,d\right )}^2\,\sqrt {d+e\,x}\,\left (640\,g\,b^5\,e^5-7552\,g\,b^4\,c\,d\,e^4-1088\,f\,b^4\,c\,e^5+36048\,g\,b^3\,c^2\,d^2\,e^3+12512\,f\,b^3\,c^2\,d\,e^4-86912\,g\,b^2\,c^3\,d^3\,e^2-57528\,f\,b^2\,c^3\,d^2\,e^3+104843\,g\,b\,c^4\,d^4\,e+130492\,f\,b\,c^4\,d^3\,e^2-47067\,g\,c^5\,d^5+243797\,f\,c^5\,d^4\,e\right )}{765765\,c^5\,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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