Optimal. Leaf size=419 \[ -\frac {256 (2 c d-b e)^4 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (-2 b e g+c d g+3 c e f)}{45045 c^6 e^2 (d+e x)^{5/2}}-\frac {128 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (-2 b e g+c d g+3 c e f)}{9009 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (-2 b e g+c d g+3 c e f)}{1287 c^4 e^2 \sqrt {d+e x}}-\frac {16 \sqrt {d+e x} (2 c d-b e) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (-2 b e g+c d g+3 c e f)}{429 c^3 e^2}-\frac {2 (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (-2 b e g+c d g+3 c e f)}{39 c^2 e^2}-\frac {2 g (d+e x)^{5/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{15 c e^2} \]
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Rubi [A] time = 0.73, antiderivative size = 419, 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 )^{5/2} (-2 b e g+c d g+3 c e f)}{45045 c^6 e^2 (d+e x)^{5/2}}-\frac {128 (2 c d-b e)^3 \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (-2 b e g+c d g+3 c e f)}{9009 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 )^{5/2} (-2 b e g+c d g+3 c e f)}{1287 c^4 e^2 \sqrt {d+e x}}-\frac {16 \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 )^{5/2} (-2 b e g+c d g+3 c e f)}{429 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 )^{5/2} (-2 b e g+c d g+3 c e f)}{39 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 )^{5/2}}{15 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 )^{3/2} \, 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 )^{5/2}}{15 c e^2}-\frac {\left (2 \left (\frac {5}{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 )^{3/2} \, dx}{15 c e^3}\\ &=-\frac {2 (3 c e f+c d g-2 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{39 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 )^{5/2}}{15 c e^2}+\frac {(8 (2 c d-b e) (3 c e f+c d g-2 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 )^{3/2} \, dx}{39 c^2 e}\\ &=-\frac {16 (2 c d-b e) (3 c e f+c d g-2 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{429 c^3 e^2}-\frac {2 (3 c e f+c d g-2 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{39 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 )^{5/2}}{15 c e^2}+\frac {\left (16 (2 c d-b e)^2 (3 c e f+c d g-2 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 )^{3/2} \, dx}{143 c^3 e}\\ &=-\frac {32 (2 c d-b e)^2 (3 c e f+c d g-2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{1287 c^4 e^2 \sqrt {d+e x}}-\frac {16 (2 c d-b e) (3 c e f+c d g-2 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{429 c^3 e^2}-\frac {2 (3 c e f+c d g-2 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{39 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 )^{5/2}}{15 c e^2}+\frac {\left (64 (2 c d-b e)^3 (3 c e f+c d g-2 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{3/2}}{\sqrt {d+e x}} \, dx}{1287 c^4 e}\\ &=-\frac {128 (2 c d-b e)^3 (3 c e f+c d g-2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{9009 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 (3 c e f+c d g-2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{1287 c^4 e^2 \sqrt {d+e x}}-\frac {16 (2 c d-b e) (3 c e f+c d g-2 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{429 c^3 e^2}-\frac {2 (3 c e f+c d g-2 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{39 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 )^{5/2}}{15 c e^2}+\frac {\left (128 (2 c d-b e)^4 (3 c e f+c d g-2 b e g)\right ) \int \frac {\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{3/2}}{(d+e x)^{3/2}} \, dx}{9009 c^5 e}\\ &=-\frac {256 (2 c d-b e)^4 (3 c e f+c d g-2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{45045 c^6 e^2 (d+e x)^{5/2}}-\frac {128 (2 c d-b e)^3 (3 c e f+c d g-2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{9009 c^5 e^2 (d+e x)^{3/2}}-\frac {32 (2 c d-b e)^2 (3 c e f+c d g-2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{1287 c^4 e^2 \sqrt {d+e x}}-\frac {16 (2 c d-b e) (3 c e f+c d g-2 b e g) \sqrt {d+e x} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{429 c^3 e^2}-\frac {2 (3 c e f+c d g-2 b e g) (d+e x)^{3/2} \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{39 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 )^{5/2}}{15 c e^2}\\ \end {align*}
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Mathematica [A] time = 0.35, size = 364, normalized size = 0.87 \begin {gather*} -\frac {2 (b e-c d+c e x)^2 \sqrt {(d+e x) (c (d-e x)-b e)} \left (-256 b^5 e^5 g+128 b^4 c e^4 (22 d g+3 e f+5 e g x)-32 b^3 c^2 e^3 \left (389 d^2 g+2 d e (63 f+100 g x)+5 e^2 x (6 f+7 g x)\right )+16 b^2 c^3 e^2 \left (1724 d^3 g+3 d^2 e (347 f+515 g x)+30 d e^2 x (19 f+21 g x)+105 e^3 x^2 (f+g x)\right )-2 b c^4 e \left (15191 d^4 g+4 d^3 e (4131 f+5530 g x)+30 d^2 e^2 x (542 f+553 g x)+420 d e^3 x^2 (17 f+16 g x)+105 e^4 x^3 (12 f+11 g x)\right )+c^5 \left (12686 d^5 g+d^4 e (29049 f+31715 g x)+20 d^3 e^2 x (2505 f+2212 g x)+210 d^2 e^3 x^2 (203 f+173 g x)+210 d e^4 x^3 (90 f+77 g x)+231 e^5 x^4 (15 f+13 g x)\right )\right )}{45045 c^6 e^2 \sqrt {d+e x}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 8.65, size = 598, normalized size = 1.43 \begin {gather*} -\frac {2 \left ((d+e x) (2 c d-b e)-c (d+e x)^2\right )^{5/2} \left (-256 b^5 e^5 g+640 b^4 c e^4 g (d+e x)+2176 b^4 c d e^4 g+384 b^4 c e^5 f-7168 b^3 c^2 d^2 e^3 g-960 b^3 c^2 e^4 f (d+e x)-3072 b^3 c^2 d e^4 f-1120 b^3 c^2 e^3 g (d+e x)^2-4160 b^3 c^2 d e^3 g (d+e x)+11264 b^2 c^3 d^3 e^2 g+9216 b^2 c^3 d^2 e^3 f+9600 b^2 c^3 d^2 e^2 g (d+e x)+1680 b^2 c^3 e^3 f (d+e x)^2+5760 b^2 c^3 d e^3 f (d+e x)+1680 b^2 c^3 e^2 g (d+e x)^3+5040 b^2 c^3 d e^2 g (d+e x)^2-8192 b c^4 d^4 e g-12288 b c^4 d^3 e^2 f-8960 b c^4 d^3 e g (d+e x)-11520 b c^4 d^2 e^2 f (d+e x)-6720 b c^4 d^2 e g (d+e x)^2-2520 b c^4 e^2 f (d+e x)^3-6720 b c^4 d e^2 f (d+e x)^2-2310 b c^4 e g (d+e x)^4-4200 b c^4 d e g (d+e x)^3+2048 c^5 d^5 g+6144 c^5 d^4 e f+2560 c^5 d^4 g (d+e x)+7680 c^5 d^3 e f (d+e x)+2240 c^5 d^3 g (d+e x)^2+6720 c^5 d^2 e f (d+e x)^2+1680 c^5 d^2 g (d+e x)^3+3465 c^5 e f (d+e x)^4+5040 c^5 d e f (d+e x)^3+3003 c^5 g (d+e x)^5+1155 c^5 d g (d+e x)^4\right )}{45045 c^6 e^2 (d+e x)^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.45, size = 880, normalized size = 2.10 \begin {gather*} -\frac {2 \, {\left (3003 \, c^{7} e^{7} g x^{7} + 231 \, {\left (15 \, c^{7} e^{7} f + 4 \, {\left (11 \, c^{7} d e^{6} + 4 \, b c^{6} e^{7}\right )} g\right )} x^{6} + 63 \, {\left (10 \, {\left (19 \, c^{7} d e^{6} + 7 \, b c^{6} e^{7}\right )} f + {\left (111 \, c^{7} d^{2} e^{5} + 278 \, b c^{6} d e^{6} + b^{2} c^{5} e^{7}\right )} g\right )} x^{5} + 35 \, {\left (3 \, {\left (79 \, c^{7} d^{2} e^{5} + 206 \, b c^{6} d e^{6} + b^{2} c^{5} e^{7}\right )} f - 2 \, {\left (175 \, c^{7} d^{3} e^{4} - 453 \, b c^{6} d^{2} e^{5} - 9 \, b^{2} c^{5} d e^{6} + b^{3} c^{4} e^{7}\right )} g\right )} x^{4} - 5 \, {\left (12 \, {\left (271 \, c^{7} d^{3} e^{4} - 683 \, b c^{6} d^{2} e^{5} - 19 \, b^{2} c^{5} d e^{6} + 2 \, b^{3} c^{4} e^{7}\right )} f + {\left (4087 \, c^{7} d^{4} e^{3} - 4900 \, b c^{6} d^{3} e^{4} - 618 \, b^{2} c^{5} d^{2} e^{5} + 160 \, b^{3} c^{4} d e^{6} - 16 \, b^{4} c^{3} e^{7}\right )} g\right )} x^{3} - 3 \, {\left (3 \, {\left (3169 \, c^{7} d^{4} e^{3} - 3628 \, b c^{6} d^{3} e^{4} - 694 \, b^{2} c^{5} d^{2} e^{5} + 168 \, b^{3} c^{4} d e^{6} - 16 \, b^{4} c^{3} e^{7}\right )} f + 4 \, {\left (542 \, c^{7} d^{5} e^{2} + 11 \, b c^{6} d^{4} e^{3} - 862 \, b^{2} c^{5} d^{3} e^{4} + 389 \, b^{3} c^{4} d^{2} e^{5} - 88 \, b^{4} c^{3} d e^{6} + 8 \, b^{5} c^{2} e^{7}\right )} g\right )} x^{2} + 3 \, {\left (9683 \, c^{7} d^{6} e - 30382 \, b c^{6} d^{5} e^{2} + 37267 \, b^{2} c^{5} d^{4} e^{3} - 23464 \, b^{3} c^{4} d^{3} e^{4} + 8368 \, b^{4} c^{3} d^{2} e^{5} - 1600 \, b^{5} c^{2} d e^{6} + 128 \, b^{6} c e^{7}\right )} f + 2 \, {\left (6343 \, c^{7} d^{7} - 27877 \, b c^{6} d^{6} e + 50517 \, b^{2} c^{5} d^{5} e^{2} - 48999 \, b^{3} c^{4} d^{4} e^{3} + 27648 \, b^{4} c^{3} d^{3} e^{4} - 9168 \, b^{5} c^{2} d^{2} e^{5} + 1664 \, b^{6} c d e^{6} - 128 \, b^{7} e^{7}\right )} g - {\left (6 \, {\left (1333 \, c^{7} d^{5} e^{2} + 1421 \, b c^{6} d^{4} e^{3} - 4142 \, b^{2} c^{5} d^{3} e^{4} + 1724 \, b^{3} c^{4} d^{2} e^{5} - 368 \, b^{4} c^{3} d e^{6} + 32 \, b^{5} c^{2} e^{7}\right )} f - {\left (6343 \, c^{7} d^{6} e - 21534 \, b c^{6} d^{5} e^{2} + 28983 \, b^{2} c^{5} d^{4} e^{3} - 20016 \, b^{3} c^{4} d^{3} e^{4} + 7632 \, b^{4} c^{3} d^{2} e^{5} - 1536 \, b^{5} c^{2} d e^{6} + 128 \, b^{6} c e^{7}\right )} g\right )} x\right )} \sqrt {-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e} \sqrt {e x + d}}{45045 \, {\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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giac [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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maple [A] time = 0.05, size = 535, normalized size = 1.28 \begin {gather*} -\frac {2 \left (c e x +b e -c d \right ) \left (-3003 g \,e^{5} x^{5} c^{5}+2310 b \,c^{4} e^{5} g \,x^{4}-16170 c^{5} d \,e^{4} g \,x^{4}-3465 c^{5} e^{5} f \,x^{4}-1680 b^{2} c^{3} e^{5} g \,x^{3}+13440 b \,c^{4} d \,e^{4} g \,x^{3}+2520 b \,c^{4} e^{5} f \,x^{3}-36330 c^{5} d^{2} e^{3} g \,x^{3}-18900 c^{5} d \,e^{4} f \,x^{3}+1120 b^{3} c^{2} e^{5} g \,x^{2}-10080 b^{2} c^{3} d \,e^{4} g \,x^{2}-1680 b^{2} c^{3} e^{5} f \,x^{2}+33180 b \,c^{4} d^{2} e^{3} g \,x^{2}+14280 b \,c^{4} d \,e^{4} f \,x^{2}-44240 c^{5} d^{3} e^{2} g \,x^{2}-42630 c^{5} d^{2} e^{3} f \,x^{2}-640 b^{4} c \,e^{5} g x +6400 b^{3} c^{2} d \,e^{4} g x +960 b^{3} c^{2} e^{5} f x -24720 b^{2} c^{3} d^{2} e^{3} g x -9120 b^{2} c^{3} d \,e^{4} f x +44240 b \,c^{4} d^{3} e^{2} g x +32520 b \,c^{4} d^{2} e^{3} f x -31715 c^{5} d^{4} e g x -50100 c^{5} d^{3} e^{2} f x +256 b^{5} e^{5} g -2816 b^{4} c d \,e^{4} g -384 b^{4} c \,e^{5} f +12448 b^{3} c^{2} d^{2} e^{3} g +4032 b^{3} c^{2} d \,e^{4} f -27584 b^{2} c^{3} d^{3} e^{2} g -16656 b^{2} c^{3} d^{2} e^{3} f +30382 b \,c^{4} d^{4} e g +33048 b \,c^{4} d^{3} e^{2} f -12686 c^{5} d^{5} g -29049 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 {3}{2}}}{45045 \left (e x +d \right )^{\frac {3}{2}} c^{6} e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.10, size = 875, normalized size = 2.09 \begin {gather*} -\frac {2 \, {\left (1155 \, c^{6} e^{6} x^{6} + 9683 \, c^{6} d^{6} - 30382 \, b c^{5} d^{5} e + 37267 \, b^{2} c^{4} d^{4} e^{2} - 23464 \, b^{3} c^{3} d^{3} e^{3} + 8368 \, b^{4} c^{2} d^{2} e^{4} - 1600 \, b^{5} c d e^{5} + 128 \, b^{6} e^{6} + 210 \, {\left (19 \, c^{6} d e^{5} + 7 \, b c^{5} e^{6}\right )} x^{5} + 35 \, {\left (79 \, c^{6} d^{2} e^{4} + 206 \, b c^{5} d e^{5} + b^{2} c^{4} e^{6}\right )} x^{4} - 20 \, {\left (271 \, c^{6} d^{3} e^{3} - 683 \, b c^{5} d^{2} e^{4} - 19 \, b^{2} c^{4} d e^{5} + 2 \, b^{3} c^{3} e^{6}\right )} x^{3} - 3 \, {\left (3169 \, c^{6} d^{4} e^{2} - 3628 \, b c^{5} d^{3} e^{3} - 694 \, b^{2} c^{4} d^{2} e^{4} + 168 \, b^{3} c^{3} d e^{5} - 16 \, b^{4} c^{2} e^{6}\right )} x^{2} - 2 \, {\left (1333 \, c^{6} d^{5} e + 1421 \, b c^{5} d^{4} e^{2} - 4142 \, b^{2} c^{4} d^{3} e^{3} + 1724 \, b^{3} c^{3} d^{2} e^{4} - 368 \, b^{4} c^{2} d e^{5} + 32 \, b^{5} c e^{6}\right )} x\right )} \sqrt {-c e x + c d - b e} {\left (e x + d\right )} f}{15015 \, {\left (c^{5} e^{2} x + c^{5} d e\right )}} - \frac {2 \, {\left (3003 \, c^{7} e^{7} x^{7} + 12686 \, c^{7} d^{7} - 55754 \, b c^{6} d^{6} e + 101034 \, b^{2} c^{5} d^{5} e^{2} - 97998 \, b^{3} c^{4} d^{4} e^{3} + 55296 \, b^{4} c^{3} d^{3} e^{4} - 18336 \, b^{5} c^{2} d^{2} e^{5} + 3328 \, b^{6} c d e^{6} - 256 \, b^{7} e^{7} + 924 \, {\left (11 \, c^{7} d e^{6} + 4 \, b c^{6} e^{7}\right )} x^{6} + 63 \, {\left (111 \, c^{7} d^{2} e^{5} + 278 \, b c^{6} d e^{6} + b^{2} c^{5} e^{7}\right )} x^{5} - 70 \, {\left (175 \, c^{7} d^{3} e^{4} - 453 \, b c^{6} d^{2} e^{5} - 9 \, b^{2} c^{5} d e^{6} + b^{3} c^{4} e^{7}\right )} x^{4} - 5 \, {\left (4087 \, c^{7} d^{4} e^{3} - 4900 \, b c^{6} d^{3} e^{4} - 618 \, b^{2} c^{5} d^{2} e^{5} + 160 \, b^{3} c^{4} d e^{6} - 16 \, b^{4} c^{3} e^{7}\right )} x^{3} - 12 \, {\left (542 \, c^{7} d^{5} e^{2} + 11 \, b c^{6} d^{4} e^{3} - 862 \, b^{2} c^{5} d^{3} e^{4} + 389 \, b^{3} c^{4} d^{2} e^{5} - 88 \, b^{4} c^{3} d e^{6} + 8 \, b^{5} c^{2} e^{7}\right )} x^{2} + {\left (6343 \, c^{7} d^{6} e - 21534 \, b c^{6} d^{5} e^{2} + 28983 \, b^{2} c^{5} d^{4} e^{3} - 20016 \, b^{3} c^{4} d^{3} e^{4} + 7632 \, b^{4} c^{3} d^{2} e^{5} - 1536 \, b^{5} c^{2} d e^{6} + 128 \, b^{6} c e^{7}\right )} x\right )} \sqrt {-c e x + c d - b e} {\left (e x + d\right )} g}{45045 \, {\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 = 3.93, size = 863, normalized size = 2.06 \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 (16\,b\,e\,g+44\,c\,d\,g+15\,c\,e\,f\right )}{195}+\frac {2\,e^2\,x^5\,\sqrt {d+e\,x}\,\left (g\,b^2\,e^2+278\,g\,b\,c\,d\,e+70\,f\,b\,c\,e^2+111\,g\,c^2\,d^2+190\,f\,c^2\,d\,e\right )}{715\,c}+\frac {2\,c\,e^4\,g\,x^7\,\sqrt {d+e\,x}}{15}+\frac {2\,{\left (b\,e-c\,d\right )}^2\,\sqrt {d+e\,x}\,\left (-256\,g\,b^5\,e^5+2816\,g\,b^4\,c\,d\,e^4+384\,f\,b^4\,c\,e^5-12448\,g\,b^3\,c^2\,d^2\,e^3-4032\,f\,b^3\,c^2\,d\,e^4+27584\,g\,b^2\,c^3\,d^3\,e^2+16656\,f\,b^2\,c^3\,d^2\,e^3-30382\,g\,b\,c^4\,d^4\,e-33048\,f\,b\,c^4\,d^3\,e^2+12686\,g\,c^5\,d^5+29049\,f\,c^5\,d^4\,e\right )}{45045\,c^6\,e^3}+\frac {x^3\,\sqrt {d+e\,x}\,\left (160\,g\,b^4\,c^3\,e^7-1600\,g\,b^3\,c^4\,d\,e^6-240\,f\,b^3\,c^4\,e^7+6180\,g\,b^2\,c^5\,d^2\,e^5+2280\,f\,b^2\,c^5\,d\,e^6+49000\,g\,b\,c^6\,d^3\,e^4+81960\,f\,b\,c^6\,d^2\,e^5-40870\,g\,c^7\,d^4\,e^3-32520\,f\,c^7\,d^3\,e^4\right )}{45045\,c^6\,e^3}+\frac {x^4\,\sqrt {d+e\,x}\,\left (-140\,g\,b^3\,c^4\,e^7+1260\,g\,b^2\,c^5\,d\,e^6+210\,f\,b^2\,c^5\,e^7+63420\,g\,b\,c^6\,d^2\,e^5+43260\,f\,b\,c^6\,d\,e^6-24500\,g\,c^7\,d^3\,e^4+16590\,f\,c^7\,d^2\,e^5\right )}{45045\,c^6\,e^3}-\frac {x^2\,\sqrt {d+e\,x}\,\left (192\,g\,b^5\,c^2\,e^7-2112\,g\,b^4\,c^3\,d\,e^6-288\,f\,b^4\,c^3\,e^7+9336\,g\,b^3\,c^4\,d^2\,e^5+3024\,f\,b^3\,c^4\,d\,e^6-20688\,g\,b^2\,c^5\,d^3\,e^4-12492\,f\,b^2\,c^5\,d^2\,e^5+264\,g\,b\,c^6\,d^4\,e^3-65304\,f\,b\,c^6\,d^3\,e^4+13008\,g\,c^7\,d^5\,e^2+57042\,f\,c^7\,d^4\,e^3\right )}{45045\,c^6\,e^3}+\frac {2\,x\,\left (b\,e-c\,d\right )\,\sqrt {d+e\,x}\,\left (128\,g\,b^5\,e^5-1408\,g\,b^4\,c\,d\,e^4-192\,f\,b^4\,c\,e^5+6224\,g\,b^3\,c^2\,d^2\,e^3+2016\,f\,b^3\,c^2\,d\,e^4-13792\,g\,b^2\,c^3\,d^3\,e^2-8328\,f\,b^2\,c^3\,d^2\,e^3+15191\,g\,b\,c^4\,d^4\,e+16524\,f\,b\,c^4\,d^3\,e^2-6343\,g\,c^5\,d^5+7998\,f\,c^5\,d^4\,e\right )}{45045\,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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