Optimal. Leaf size=436 \[ \frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}+\frac {\left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) \sqrt {a+b x} \sqrt {c+d x}}{3840 a^4 c^2 x^2}-\frac {\left (315 b^5 c^5-945 a b^4 c^4 d+838 a^2 b^3 c^3 d^2-90 a^3 b^2 c^2 d^3-65 a^4 b c d^4+75 a^5 d^5\right ) \sqrt {a+b x} \sqrt {c+d x}}{7680 a^5 c^3 x}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}+\frac {(b c-a d)^4 \left (21 b^2 c^2+14 a b c d+5 a^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {a+b x}}{\sqrt {a} \sqrt {c+d x}}\right )}{512 a^{11/2} c^{7/2}} \]
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Rubi [A]
time = 0.33, antiderivative size = 436, normalized size of antiderivative = 1.00, number of steps
used = 9, number of rules used = 6, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {99, 154, 156,
12, 95, 214} \begin {gather*} \frac {\sqrt {a+b x} \sqrt {c+d x} \left (-5 a^2 d^2-6 a b c d+3 b^2 c^2\right )}{160 a^2 x^4}+\frac {\left (5 a^2 d^2+14 a b c d+21 b^2 c^2\right ) (b c-a d)^4 \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {a+b x}}{\sqrt {a} \sqrt {c+d x}}\right )}{512 a^{11/2} c^{7/2}}-\frac {\sqrt {a+b x} \sqrt {c+d x} \left (5 a^3 d^3+51 a^2 b c d^2-61 a b^2 c^2 d+21 b^3 c^3\right )}{960 a^3 c x^3}+\frac {\sqrt {a+b x} \sqrt {c+d x} \left (25 a^4 d^4-20 a^3 b c d^3+262 a^2 b^2 c^2 d^2-308 a b^3 c^3 d+105 b^4 c^4\right )}{3840 a^4 c^2 x^2}-\frac {\sqrt {a+b x} \sqrt {c+d x} \left (75 a^5 d^5-65 a^4 b c d^4-90 a^3 b^2 c^2 d^3+838 a^2 b^3 c^3 d^2-945 a b^4 c^4 d+315 b^5 c^5\right )}{7680 a^5 c^3 x}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}-\frac {\sqrt {a+b x} (c+d x)^{3/2} (5 a d+b c)}{60 a x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 95
Rule 99
Rule 154
Rule 156
Rule 214
Rubi steps
\begin {align*} \int \frac {\sqrt {a+b x} (c+d x)^{5/2}}{x^7} \, dx &=-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}+\frac {1}{6} \int \frac {(c+d x)^{3/2} \left (\frac {1}{2} (b c+5 a d)+3 b d x\right )}{x^6 \sqrt {a+b x}} \, dx\\ &=-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}+\frac {\int \frac {\sqrt {c+d x} \left (-\frac {3}{4} \left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right )-\frac {3}{2} b d (b c-5 a d) x\right )}{x^5 \sqrt {a+b x}} \, dx}{30 a}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}+\frac {\int \frac {\frac {3}{8} \left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right )+\frac {3}{4} b d \left (9 b^2 c^2-26 a b c d+25 a^2 d^2\right ) x}{x^4 \sqrt {a+b x} \sqrt {c+d x}} \, dx}{120 a^2}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}-\frac {\int \frac {\frac {3}{16} \left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right )+\frac {3}{4} b d \left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) x}{x^3 \sqrt {a+b x} \sqrt {c+d x}} \, dx}{360 a^3 c}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}+\frac {\left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) \sqrt {a+b x} \sqrt {c+d x}}{3840 a^4 c^2 x^2}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}+\frac {\int \frac {\frac {3}{32} \left (315 b^5 c^5-945 a b^4 c^4 d+838 a^2 b^3 c^3 d^2-90 a^3 b^2 c^2 d^3-65 a^4 b c d^4+75 a^5 d^5\right )+\frac {3}{16} b d \left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) x}{x^2 \sqrt {a+b x} \sqrt {c+d x}} \, dx}{720 a^4 c^2}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}+\frac {\left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) \sqrt {a+b x} \sqrt {c+d x}}{3840 a^4 c^2 x^2}-\frac {\left (315 b^5 c^5-945 a b^4 c^4 d+838 a^2 b^3 c^3 d^2-90 a^3 b^2 c^2 d^3-65 a^4 b c d^4+75 a^5 d^5\right ) \sqrt {a+b x} \sqrt {c+d x}}{7680 a^5 c^3 x}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}-\frac {\int \frac {45 (b c-a d)^4 \left (21 b^2 c^2+14 a b c d+5 a^2 d^2\right )}{64 x \sqrt {a+b x} \sqrt {c+d x}} \, dx}{720 a^5 c^3}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}+\frac {\left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) \sqrt {a+b x} \sqrt {c+d x}}{3840 a^4 c^2 x^2}-\frac {\left (315 b^5 c^5-945 a b^4 c^4 d+838 a^2 b^3 c^3 d^2-90 a^3 b^2 c^2 d^3-65 a^4 b c d^4+75 a^5 d^5\right ) \sqrt {a+b x} \sqrt {c+d x}}{7680 a^5 c^3 x}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}-\frac {\left ((b c-a d)^4 \left (21 b^2 c^2+14 a b c d+5 a^2 d^2\right )\right ) \int \frac {1}{x \sqrt {a+b x} \sqrt {c+d x}} \, dx}{1024 a^5 c^3}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}+\frac {\left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) \sqrt {a+b x} \sqrt {c+d x}}{3840 a^4 c^2 x^2}-\frac {\left (315 b^5 c^5-945 a b^4 c^4 d+838 a^2 b^3 c^3 d^2-90 a^3 b^2 c^2 d^3-65 a^4 b c d^4+75 a^5 d^5\right ) \sqrt {a+b x} \sqrt {c+d x}}{7680 a^5 c^3 x}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}-\frac {\left ((b c-a d)^4 \left (21 b^2 c^2+14 a b c d+5 a^2 d^2\right )\right ) \text {Subst}\left (\int \frac {1}{-a+c x^2} \, dx,x,\frac {\sqrt {a+b x}}{\sqrt {c+d x}}\right )}{512 a^5 c^3}\\ &=\frac {\left (3 b^2 c^2-6 a b c d-5 a^2 d^2\right ) \sqrt {a+b x} \sqrt {c+d x}}{160 a^2 x^4}-\frac {\left (21 b^3 c^3-61 a b^2 c^2 d+51 a^2 b c d^2+5 a^3 d^3\right ) \sqrt {a+b x} \sqrt {c+d x}}{960 a^3 c x^3}+\frac {\left (105 b^4 c^4-308 a b^3 c^3 d+262 a^2 b^2 c^2 d^2-20 a^3 b c d^3+25 a^4 d^4\right ) \sqrt {a+b x} \sqrt {c+d x}}{3840 a^4 c^2 x^2}-\frac {\left (315 b^5 c^5-945 a b^4 c^4 d+838 a^2 b^3 c^3 d^2-90 a^3 b^2 c^2 d^3-65 a^4 b c d^4+75 a^5 d^5\right ) \sqrt {a+b x} \sqrt {c+d x}}{7680 a^5 c^3 x}-\frac {(b c+5 a d) \sqrt {a+b x} (c+d x)^{3/2}}{60 a x^5}-\frac {\sqrt {a+b x} (c+d x)^{5/2}}{6 x^6}+\frac {(b c-a d)^4 \left (21 b^2 c^2+14 a b c d+5 a^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {a+b x}}{\sqrt {a} \sqrt {c+d x}}\right )}{512 a^{11/2} c^{7/2}}\\ \end {align*}
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Mathematica [A]
time = 0.88, size = 323, normalized size = 0.74 \begin {gather*} -\frac {\sqrt {a+b x} \sqrt {c+d x} \left (315 b^5 c^5 x^5-105 a b^4 c^4 x^4 (2 c+9 d x)+2 a^2 b^3 c^3 x^3 \left (84 c^2+308 c d x+419 d^2 x^2\right )-2 a^3 b^2 c^2 x^2 \left (72 c^3+244 c^2 d x+262 c d^2 x^2+45 d^3 x^3\right )+a^4 b c x \left (128 c^4+416 c^3 d x+408 c^2 d^2 x^2+40 c d^3 x^3-65 d^4 x^4\right )+5 a^5 \left (256 c^5+640 c^4 d x+432 c^3 d^2 x^2+8 c^2 d^3 x^3-10 c d^4 x^4+15 d^5 x^5\right )\right )}{7680 a^5 c^3 x^6}+\frac {(b c-a d)^4 \left (21 b^2 c^2+14 a b c d+5 a^2 d^2\right ) \tanh ^{-1}\left (\frac {\sqrt {c} \sqrt {a+b x}}{\sqrt {a} \sqrt {c+d x}}\right )}{512 a^{11/2} c^{7/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1067\) vs.
\(2(386)=772\).
time = 0.08, size = 1068, normalized size = 2.45
method | result | size |
default | \(\frac {\sqrt {d x +c}\, \sqrt {b x +a}\, \left (130 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{4} b c \,d^{4} x^{5}+180 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{3} b^{2} c^{2} d^{3} x^{5}-1676 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{2} b^{3} c^{3} d^{2} x^{5}+1890 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a \,b^{4} c^{4} d \,x^{5}-90 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) a^{5} b c \,d^{5} x^{6}-75 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) a^{4} b^{2} c^{2} d^{4} x^{6}-300 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) a^{3} b^{3} c^{3} d^{3} x^{6}+1125 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) a^{2} b^{4} c^{4} d^{2} x^{6}-1050 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) a \,b^{5} c^{5} d \,x^{6}-80 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{5} c^{2} d^{3} x^{3}-336 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{2} b^{3} c^{5} x^{3}-4320 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{5} c^{3} d^{2} x^{2}-6400 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{5} c^{4} d x -256 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{4} b \,c^{5} x +100 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{5} c \,d^{4} x^{4}+420 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a \,b^{4} c^{5} x^{4}+288 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{3} b^{2} c^{5} x^{2}-2560 \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{5} c^{5} \sqrt {a c}+75 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) a^{6} d^{6} x^{6}+315 \ln \left (\frac {a d x +b c x +2 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}+2 a c}{x}\right ) b^{6} c^{6} x^{6}-80 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{4} b \,c^{2} d^{3} x^{4}+1048 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{3} b^{2} c^{3} d^{2} x^{4}-1232 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{2} b^{3} c^{4} d \,x^{4}-816 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{4} b \,c^{3} d^{2} x^{3}+976 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{3} b^{2} c^{4} d \,x^{3}-832 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{4} b \,c^{4} d \,x^{2}-630 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, b^{5} c^{5} x^{5}-150 \sqrt {a c}\, \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, a^{5} d^{5} x^{5}\right )}{15360 a^{5} c^{3} \sqrt {\left (d x +c \right ) \left (b x +a \right )}\, x^{6} \sqrt {a c}}\) | \(1068\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 11.91, size = 918, normalized size = 2.11 \begin {gather*} \left [\frac {15 \, {\left (21 \, b^{6} c^{6} - 70 \, a b^{5} c^{5} d + 75 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 5 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + 5 \, a^{6} d^{6}\right )} \sqrt {a c} x^{6} \log \left (\frac {8 \, a^{2} c^{2} + {\left (b^{2} c^{2} + 6 \, a b c d + a^{2} d^{2}\right )} x^{2} + 4 \, {\left (2 \, a c + {\left (b c + a d\right )} x\right )} \sqrt {a c} \sqrt {b x + a} \sqrt {d x + c} + 8 \, {\left (a b c^{2} + a^{2} c d\right )} x}{x^{2}}\right ) - 4 \, {\left (1280 \, a^{6} c^{6} + {\left (315 \, a b^{5} c^{6} - 945 \, a^{2} b^{4} c^{5} d + 838 \, a^{3} b^{3} c^{4} d^{2} - 90 \, a^{4} b^{2} c^{3} d^{3} - 65 \, a^{5} b c^{2} d^{4} + 75 \, a^{6} c d^{5}\right )} x^{5} - 2 \, {\left (105 \, a^{2} b^{4} c^{6} - 308 \, a^{3} b^{3} c^{5} d + 262 \, a^{4} b^{2} c^{4} d^{2} - 20 \, a^{5} b c^{3} d^{3} + 25 \, a^{6} c^{2} d^{4}\right )} x^{4} + 8 \, {\left (21 \, a^{3} b^{3} c^{6} - 61 \, a^{4} b^{2} c^{5} d + 51 \, a^{5} b c^{4} d^{2} + 5 \, a^{6} c^{3} d^{3}\right )} x^{3} - 16 \, {\left (9 \, a^{4} b^{2} c^{6} - 26 \, a^{5} b c^{5} d - 135 \, a^{6} c^{4} d^{2}\right )} x^{2} + 128 \, {\left (a^{5} b c^{6} + 25 \, a^{6} c^{5} d\right )} x\right )} \sqrt {b x + a} \sqrt {d x + c}}{30720 \, a^{6} c^{4} x^{6}}, -\frac {15 \, {\left (21 \, b^{6} c^{6} - 70 \, a b^{5} c^{5} d + 75 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} - 5 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + 5 \, a^{6} d^{6}\right )} \sqrt {-a c} x^{6} \arctan \left (\frac {{\left (2 \, a c + {\left (b c + a d\right )} x\right )} \sqrt {-a c} \sqrt {b x + a} \sqrt {d x + c}}{2 \, {\left (a b c d x^{2} + a^{2} c^{2} + {\left (a b c^{2} + a^{2} c d\right )} x\right )}}\right ) + 2 \, {\left (1280 \, a^{6} c^{6} + {\left (315 \, a b^{5} c^{6} - 945 \, a^{2} b^{4} c^{5} d + 838 \, a^{3} b^{3} c^{4} d^{2} - 90 \, a^{4} b^{2} c^{3} d^{3} - 65 \, a^{5} b c^{2} d^{4} + 75 \, a^{6} c d^{5}\right )} x^{5} - 2 \, {\left (105 \, a^{2} b^{4} c^{6} - 308 \, a^{3} b^{3} c^{5} d + 262 \, a^{4} b^{2} c^{4} d^{2} - 20 \, a^{5} b c^{3} d^{3} + 25 \, a^{6} c^{2} d^{4}\right )} x^{4} + 8 \, {\left (21 \, a^{3} b^{3} c^{6} - 61 \, a^{4} b^{2} c^{5} d + 51 \, a^{5} b c^{4} d^{2} + 5 \, a^{6} c^{3} d^{3}\right )} x^{3} - 16 \, {\left (9 \, a^{4} b^{2} c^{6} - 26 \, a^{5} b c^{5} d - 135 \, a^{6} c^{4} d^{2}\right )} x^{2} + 128 \, {\left (a^{5} b c^{6} + 25 \, a^{6} c^{5} d\right )} x\right )} \sqrt {b x + a} \sqrt {d x + c}}{15360 \, a^{6} c^{4} x^{6}}\right ] \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
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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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 8502 vs.
\(2 (386) = 772\).
time = 6.01, size = 8502, normalized size = 19.50 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {a+b\,x}\,{\left (c+d\,x\right )}^{5/2}}{x^7} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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