Optimal. Leaf size=262 \[ \frac {120 d^3 (b c-a d)^7 x}{b^{10}}-\frac {(b c-a d)^{10}}{2 b^{11} (a+b x)^2}-\frac {10 d (b c-a d)^9}{b^{11} (a+b x)}+\frac {105 d^4 (b c-a d)^6 (a+b x)^2}{b^{11}}+\frac {84 d^5 (b c-a d)^5 (a+b x)^3}{b^{11}}+\frac {105 d^6 (b c-a d)^4 (a+b x)^4}{2 b^{11}}+\frac {24 d^7 (b c-a d)^3 (a+b x)^5}{b^{11}}+\frac {15 d^8 (b c-a d)^2 (a+b x)^6}{2 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^7}{7 b^{11}}+\frac {d^{10} (a+b x)^8}{8 b^{11}}+\frac {45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}} \]
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Rubi [A]
time = 0.30, antiderivative size = 262, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} \frac {10 d^9 (a+b x)^7 (b c-a d)}{7 b^{11}}+\frac {15 d^8 (a+b x)^6 (b c-a d)^2}{2 b^{11}}+\frac {24 d^7 (a+b x)^5 (b c-a d)^3}{b^{11}}+\frac {105 d^6 (a+b x)^4 (b c-a d)^4}{2 b^{11}}+\frac {84 d^5 (a+b x)^3 (b c-a d)^5}{b^{11}}+\frac {105 d^4 (a+b x)^2 (b c-a d)^6}{b^{11}}+\frac {45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}}-\frac {10 d (b c-a d)^9}{b^{11} (a+b x)}-\frac {(b c-a d)^{10}}{2 b^{11} (a+b x)^2}+\frac {d^{10} (a+b x)^8}{8 b^{11}}+\frac {120 d^3 x (b c-a d)^7}{b^{10}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(c+d x)^{10}}{(a+b x)^3} \, dx &=\int \left (\frac {120 d^3 (b c-a d)^7}{b^{10}}+\frac {(b c-a d)^{10}}{b^{10} (a+b x)^3}+\frac {10 d (b c-a d)^9}{b^{10} (a+b x)^2}+\frac {45 d^2 (b c-a d)^8}{b^{10} (a+b x)}+\frac {210 d^4 (b c-a d)^6 (a+b x)}{b^{10}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^2}{b^{10}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^3}{b^{10}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^4}{b^{10}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^5}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^6}{b^{10}}+\frac {d^{10} (a+b x)^7}{b^{10}}\right ) \, dx\\ &=\frac {120 d^3 (b c-a d)^7 x}{b^{10}}-\frac {(b c-a d)^{10}}{2 b^{11} (a+b x)^2}-\frac {10 d (b c-a d)^9}{b^{11} (a+b x)}+\frac {105 d^4 (b c-a d)^6 (a+b x)^2}{b^{11}}+\frac {84 d^5 (b c-a d)^5 (a+b x)^3}{b^{11}}+\frac {105 d^6 (b c-a d)^4 (a+b x)^4}{2 b^{11}}+\frac {24 d^7 (b c-a d)^3 (a+b x)^5}{b^{11}}+\frac {15 d^8 (b c-a d)^2 (a+b x)^6}{2 b^{11}}+\frac {10 d^9 (b c-a d) (a+b x)^7}{7 b^{11}}+\frac {d^{10} (a+b x)^8}{8 b^{11}}+\frac {45 d^2 (b c-a d)^8 \log (a+b x)}{b^{11}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(708\) vs. \(2(262)=524\).
time = 0.15, size = 708, normalized size = 2.70 \begin {gather*} \frac {532 a^{10} d^{10}-56 a^9 b d^9 (85 c+26 d x)+28 a^8 b^2 d^8 \left (675 c^2+380 c d x-116 d^2 x^2\right )-280 a^7 b^3 d^7 \left (156 c^3+117 c^2 d x-91 c d^2 x^2+3 d^3 x^3\right )+210 a^6 b^4 d^6 \left (308 c^4+256 c^3 d x-414 c^2 d^2 x^2+32 c d^3 x^3+d^4 x^4\right )-84 a^5 b^5 d^5 \left (756 c^5+560 c^4 d x-2000 c^3 d^2 x^2+280 c^2 d^3 x^3+20 c d^4 x^4+d^5 x^5\right )+42 a^4 b^6 d^4 \left (980 c^6+336 c^5 d x-4760 c^4 d^2 x^2+1120 c^3 d^3 x^3+140 c^2 d^4 x^4+16 c d^5 x^5+d^6 x^6\right )-24 a^3 b^7 d^3 \left (700 c^7-490 c^6 d x-6174 c^5 d^2 x^2+2450 c^4 d^3 x^3+490 c^3 d^4 x^4+98 c^2 d^5 x^5+14 c d^6 x^6+d^7 x^7\right )+3 a^2 b^8 d^2 \left (1260 c^8-4480 c^7 d x-21560 c^6 d^2 x^2+15680 c^5 d^3 x^3+4900 c^4 d^4 x^4+1568 c^3 d^5 x^5+392 c^2 d^6 x^6+64 c d^7 x^7+5 d^8 x^8\right )-2 a b^9 d \left (140 c^9-2520 c^8 d x-6720 c^7 d^2 x^2+11760 c^6 d^3 x^3+5880 c^5 d^4 x^4+2940 c^4 d^5 x^5+1176 c^3 d^6 x^6+336 c^2 d^7 x^7+60 c d^8 x^8+5 d^9 x^9\right )+b^{10} \left (-28 c^{10}-560 c^9 d x+6720 c^7 d^3 x^3+5880 c^6 d^4 x^4+4704 c^5 d^5 x^5+2940 c^4 d^6 x^6+1344 c^3 d^7 x^7+420 c^2 d^8 x^8+80 c d^9 x^9+7 d^{10} x^{10}\right )+2520 d^2 (b c-a d)^8 (a+b x)^2 \log (a+b x)}{56 b^{11} (a+b x)^2} \end {gather*}
Antiderivative was successfully verified.
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Mathics [B] Leaf count is larger than twice the leaf count of optimal. \(891\) vs. \(2(262)=524\).
time = 11.53, size = 889, normalized size = 3.39 \begin {gather*} \frac {2520 d^2 \text {Log}\left [a+b x\right ] \left (a^2+2 a b x+b^2 x^2\right ) \left (a d-b c\right )^8+532 a^{10} d^{10}-4760 a^9 b c d^9+18900 a^8 b^2 c^2 d^8-43680 a^7 b^3 c^3 d^7+64680 a^6 b^4 c^4 d^6-63504 a^5 b^5 c^5 d^5+41160 a^4 b^6 c^6 d^4-16800 a^3 b^7 c^7 d^3+3780 a^2 b^8 c^8 d^2-280 a b^9 c^9 d-28 b^{10} c^{10}+560 b d x \left (a^9 d^9-9 a^8 b c d^8+36 a^7 b^2 c^2 d^7-84 a^6 b^3 c^3 d^6+126 a^5 b^4 c^4 d^5-126 a^4 b^5 c^5 d^4+84 a^3 b^6 c^6 d^3-36 a^2 b^7 c^7 d^2+9 a b^8 c^8 d-b^9 c^9\right )-56 b d^3 x \left (a^2+2 a b x+b^2 x^2\right ) \left (36 a^7 d^7-280 a^6 b c d^6+945 a^5 b^2 c^2 d^5-1800 a^4 b^3 c^3 d^4+2100 a^3 b^4 c^4 d^3-1512 a^2 b^5 c^5 d^2+630 a b^6 c^6 d-120 b^7 c^7\right )+28 b^2 d^4 x^2 \left (a^2+2 a b x+b^2 x^2\right ) \left (28 a^6 d^6-210 a^5 b c d^5+675 a^4 b^2 c^2 d^4-1200 a^3 b^3 c^3 d^3+1260 a^2 b^4 c^4 d^2-756 a b^5 c^5 d+210 b^6 c^6\right )-56 b^3 d^5 x^3 \left (a^2+2 a b x+b^2 x^2\right ) \left (7 a^5 d^5-50 a^4 b c d^4+150 a^3 b^2 c^2 d^3-240 a^2 b^3 c^3 d^2+210 a b^4 c^4 d-84 b^5 c^5\right )+70 b^4 d^6 x^4 \left (a^2+2 a b x+b^2 x^2\right ) \left (3 a^4 d^4-20 a^3 b c d^3+54 a^2 b^2 c^2 d^2-72 a b^3 c^3 d+42 b^4 c^4\right )-56 b^5 d^7 x^5 \left (a^2+2 a b x+b^2 x^2\right ) \left (2 a^3 d^3-12 a^2 b c d^2+27 a b^2 c^2 d-24 b^3 c^3\right )+28 b^6 d^8 x^6 \left (a^2+2 a b x+b^2 x^2\right ) \left (2 a^2 d^2-10 a b c d+15 b^2 c^2\right )-8 b^7 d^9 x^7 \left (a^2+2 a b x+b^2 x^2\right ) \left (3 a d-10 b c\right )+7 b^8 d^{10} x^8 \left (a^2+2 a b x+b^2 x^2\right )}{56 b^{11} \left (a^2+2 a b x+b^2 x^2\right )} \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. \(913\) vs.
\(2(252)=504\).
time = 0.16, size = 914, normalized size = 3.49
method | result | size |
norman | \(\frac {\frac {135 a^{10} d^{10}-1080 a^{9} b c \,d^{9}+3780 a^{8} b^{2} c^{2} d^{8}-7560 a^{7} b^{3} c^{3} d^{7}+9450 a^{6} b^{4} c^{4} d^{6}-7560 a^{5} b^{5} c^{5} d^{5}+3780 a^{4} b^{6} c^{6} d^{4}-1080 a^{3} b^{7} c^{7} d^{3}+135 a^{2} b^{8} c^{8} d^{2}-10 a \,b^{9} c^{9} d -b^{10} c^{10}}{2 b^{11}}+\frac {d^{10} x^{10}}{8 b}+\frac {2 \left (45 a^{9} d^{10}-360 a^{8} b c \,d^{9}+1260 a^{7} b^{2} c^{2} d^{8}-2520 a^{6} b^{3} c^{3} d^{7}+3150 a^{5} b^{4} c^{4} d^{6}-2520 a^{4} b^{5} c^{5} d^{5}+1260 a^{3} b^{6} c^{6} d^{4}-360 a^{2} b^{7} c^{7} d^{3}+45 a \,b^{8} c^{8} d^{2}-5 b^{9} c^{9} d \right ) x}{b^{10}}-\frac {15 d^{3} \left (a^{7} d^{7}-8 a^{6} b c \,d^{6}+28 a^{5} b^{2} c^{2} d^{5}-56 a^{4} b^{3} c^{3} d^{4}+70 a^{3} b^{4} c^{4} d^{3}-56 a^{2} b^{5} c^{5} d^{2}+28 a \,b^{6} c^{6} d -8 b^{7} c^{7}\right ) x^{3}}{b^{8}}+\frac {15 d^{4} \left (a^{6} d^{6}-8 a^{5} b c \,d^{5}+28 a^{4} b^{2} c^{2} d^{4}-56 a^{3} b^{3} c^{3} d^{3}+70 a^{2} b^{4} c^{4} d^{2}-56 a \,b^{5} c^{5} d +28 b^{6} c^{6}\right ) x^{4}}{4 b^{7}}-\frac {3 d^{5} \left (a^{5} d^{5}-8 a^{4} b c \,d^{4}+28 a^{3} b^{2} c^{2} d^{3}-56 a^{2} b^{3} c^{3} d^{2}+70 a \,b^{4} c^{4} d -56 b^{5} c^{5}\right ) x^{5}}{2 b^{6}}+\frac {3 d^{6} \left (a^{4} d^{4}-8 a^{3} b c \,d^{3}+28 a^{2} b^{2} c^{2} d^{2}-56 a \,b^{3} c^{3} d +70 b^{4} c^{4}\right ) x^{6}}{4 b^{5}}-\frac {3 d^{7} \left (a^{3} d^{3}-8 a^{2} b c \,d^{2}+28 a \,b^{2} c^{2} d -56 b^{3} c^{3}\right ) x^{7}}{7 b^{4}}+\frac {15 d^{8} \left (a^{2} d^{2}-8 a b c d +28 b^{2} c^{2}\right ) x^{8}}{56 b^{3}}-\frac {5 d^{9} \left (a d -8 b c \right ) x^{9}}{28 b^{2}}}{\left (b x +a \right )^{2}}+\frac {45 d^{2} \left (a^{8} d^{8}-8 a^{7} b c \,d^{7}+28 a^{6} b^{2} c^{2} d^{6}-56 a^{5} b^{3} c^{3} d^{5}+70 a^{4} b^{4} c^{4} d^{4}-56 a^{3} b^{5} c^{5} d^{3}+28 a^{2} b^{6} c^{6} d^{2}-8 a \,b^{7} c^{7} d +b^{8} c^{8}\right ) \ln \left (b x +a \right )}{b^{11}}\) | \(838\) |
default | \(-\frac {d^{3} \left (36 a^{7} d^{7} x -120 b^{7} c^{7} x -\frac {15}{4} a^{4} b^{3} d^{7} x^{4}-\frac {105}{2} b^{7} c^{4} d^{3} x^{4}+7 a^{5} b^{2} d^{7} x^{3}-84 b^{7} c^{5} d^{2} x^{3}-14 a^{6} b \,d^{7} x^{2}-\frac {1}{8} d^{7} x^{8} b^{7}-105 b^{7} c^{6} d \,x^{2}-\frac {675}{2} a^{4} b^{3} c^{2} d^{5} x^{2}+600 a^{3} b^{4} c^{3} d^{4} x^{2}-630 a^{2} b^{5} c^{4} d^{3} x^{2}+378 a \,b^{6} c^{5} d^{2} x^{2}-280 a^{6} b c \,d^{6} x +945 a^{5} b^{2} c^{2} d^{5} x -1800 a^{4} b^{3} c^{3} d^{4} x +2100 a^{3} b^{4} c^{4} d^{3} x -1512 a^{2} b^{5} c^{5} d^{2} x +630 a \,b^{6} c^{6} d x +25 a^{3} b^{4} c \,d^{6} x^{4}-\frac {135}{2} a^{2} b^{5} c^{2} d^{5} x^{4}+90 a \,b^{6} c^{3} d^{4} x^{4}-50 a^{4} b^{3} c \,d^{6} x^{3}+150 a^{3} b^{4} c^{2} d^{5} x^{3}-240 a^{2} b^{5} c^{3} d^{4} x^{3}+210 a \,b^{6} c^{4} d^{3} x^{3}+105 a^{5} b^{2} c \,d^{6} x^{2}+\frac {3}{7} a \,b^{6} d^{7} x^{7}-\frac {10}{7} b^{7} c \,d^{6} x^{7}-a^{2} b^{5} d^{7} x^{6}-\frac {15}{2} b^{7} c^{2} d^{5} x^{6}+2 a^{3} b^{4} d^{7} x^{5}-24 b^{7} c^{3} d^{4} x^{5}+27 a \,b^{6} c^{2} d^{5} x^{5}+5 a \,b^{6} c \,d^{6} x^{6}-12 a^{2} b^{5} c \,d^{6} x^{5}\right )}{b^{10}}+\frac {10 d \left (a^{9} d^{9}-9 a^{8} b c \,d^{8}+36 a^{7} b^{2} c^{2} d^{7}-84 a^{6} b^{3} c^{3} d^{6}+126 a^{5} b^{4} c^{4} d^{5}-126 a^{4} b^{5} c^{5} d^{4}+84 a^{3} b^{6} c^{6} d^{3}-36 a^{2} b^{7} c^{7} d^{2}+9 a \,b^{8} c^{8} d -b^{9} c^{9}\right )}{b^{11} \left (b x +a \right )}-\frac {a^{10} d^{10}-10 a^{9} b c \,d^{9}+45 a^{8} b^{2} c^{2} d^{8}-120 a^{7} b^{3} c^{3} d^{7}+210 a^{6} b^{4} c^{4} d^{6}-252 a^{5} b^{5} c^{5} d^{5}+210 a^{4} b^{6} c^{6} d^{4}-120 a^{3} b^{7} c^{7} d^{3}+45 a^{2} b^{8} c^{8} d^{2}-10 a \,b^{9} c^{9} d +b^{10} c^{10}}{2 b^{11} \left (b x +a \right )^{2}}+\frac {45 d^{2} \left (a^{8} d^{8}-8 a^{7} b c \,d^{7}+28 a^{6} b^{2} c^{2} d^{6}-56 a^{5} b^{3} c^{3} d^{5}+70 a^{4} b^{4} c^{4} d^{4}-56 a^{3} b^{5} c^{5} d^{3}+28 a^{2} b^{6} c^{6} d^{2}-8 a \,b^{7} c^{7} d +b^{8} c^{8}\right ) \ln \left (b x +a \right )}{b^{11}}\) | \(914\) |
risch | \(\frac {675 d^{8} a^{4} c^{2} x^{2}}{2 b^{7}}-\frac {600 d^{7} a^{3} c^{3} x^{2}}{b^{6}}-\frac {5 d^{9} a c \,x^{6}}{b^{4}}+\frac {12 d^{9} a^{2} c \,x^{5}}{b^{5}}-\frac {360 d^{9} \ln \left (b x +a \right ) a^{7} c}{b^{10}}+\frac {1260 d^{8} \ln \left (b x +a \right ) a^{6} c^{2}}{b^{9}}-\frac {2520 d^{7} \ln \left (b x +a \right ) a^{5} c^{3}}{b^{8}}+\frac {3150 d^{6} \ln \left (b x +a \right ) a^{4} c^{4}}{b^{7}}-\frac {2520 d^{5} \ln \left (b x +a \right ) a^{3} c^{5}}{b^{6}}+\frac {1260 d^{4} \ln \left (b x +a \right ) a^{2} c^{6}}{b^{5}}-\frac {360 d^{3} \ln \left (b x +a \right ) a \,c^{7}}{b^{4}}+\frac {d^{10} x^{8}}{8 b^{3}}+\frac {d^{10} a^{2} x^{6}}{b^{5}}+\frac {15 d^{8} c^{2} x^{6}}{2 b^{3}}+\frac {630 d^{6} a^{2} c^{4} x^{2}}{b^{5}}-\frac {378 d^{5} a \,c^{5} x^{2}}{b^{4}}+\frac {280 d^{9} a^{6} c x}{b^{9}}-\frac {945 d^{8} a^{5} c^{2} x}{b^{8}}+\frac {1800 d^{7} a^{4} c^{3} x}{b^{7}}-\frac {2100 d^{6} a^{3} c^{4} x}{b^{6}}+\frac {1512 d^{5} a^{2} c^{5} x}{b^{5}}-\frac {630 d^{4} a \,c^{6} x}{b^{4}}-\frac {25 d^{9} a^{3} c \,x^{4}}{b^{6}}+\frac {135 d^{8} a^{2} c^{2} x^{4}}{2 b^{5}}-\frac {90 d^{7} a \,c^{3} x^{4}}{b^{4}}+\frac {50 d^{9} a^{4} c \,x^{3}}{b^{7}}-\frac {150 d^{8} a^{3} c^{2} x^{3}}{b^{6}}+\frac {240 d^{7} a^{2} c^{3} x^{3}}{b^{5}}-\frac {210 d^{6} a \,c^{4} x^{3}}{b^{4}}-\frac {105 d^{9} a^{5} c \,x^{2}}{b^{8}}-\frac {27 d^{8} a \,c^{2} x^{5}}{b^{4}}-\frac {36 d^{10} a^{7} x}{b^{10}}+\frac {120 d^{3} c^{7} x}{b^{3}}+\frac {15 d^{10} a^{4} x^{4}}{4 b^{7}}+\frac {105 d^{6} c^{4} x^{4}}{2 b^{3}}-\frac {7 d^{10} a^{5} x^{3}}{b^{8}}+\frac {84 d^{5} c^{5} x^{3}}{b^{3}}+\frac {14 d^{10} a^{6} x^{2}}{b^{9}}+\frac {105 d^{4} c^{6} x^{2}}{b^{3}}-\frac {3 d^{10} a \,x^{7}}{7 b^{4}}+\frac {10 d^{9} c \,x^{7}}{7 b^{3}}+\frac {\left (10 a^{9} d^{10}-90 a^{8} b c \,d^{9}+360 a^{7} b^{2} c^{2} d^{8}-840 a^{6} b^{3} c^{3} d^{7}+1260 a^{5} b^{4} c^{4} d^{6}-1260 a^{4} b^{5} c^{5} d^{5}+840 a^{3} b^{6} c^{6} d^{4}-360 a^{2} b^{7} c^{7} d^{3}+90 a \,b^{8} c^{8} d^{2}-10 b^{9} c^{9} d \right ) x +\frac {19 a^{10} d^{10}-170 a^{9} b c \,d^{9}+675 a^{8} b^{2} c^{2} d^{8}-1560 a^{7} b^{3} c^{3} d^{7}+2310 a^{6} b^{4} c^{4} d^{6}-2268 a^{5} b^{5} c^{5} d^{5}+1470 a^{4} b^{6} c^{6} d^{4}-600 a^{3} b^{7} c^{7} d^{3}+135 a^{2} b^{8} c^{8} d^{2}-10 a \,b^{9} c^{9} d -b^{10} c^{10}}{2 b}}{b^{10} \left (b x +a \right )^{2}}-\frac {2 d^{10} a^{3} x^{5}}{b^{6}}+\frac {24 d^{7} c^{3} x^{5}}{b^{3}}+\frac {45 d^{10} \ln \left (b x +a \right ) a^{8}}{b^{11}}+\frac {45 d^{2} \ln \left (b x +a \right ) c^{8}}{b^{3}}\) | \(969\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 881 vs.
\(2 (252) = 504\).
time = 0.28, size = 881, normalized size = 3.36 \begin {gather*} -\frac {b^{10} c^{10} + 10 \, a b^{9} c^{9} d - 135 \, a^{2} b^{8} c^{8} d^{2} + 600 \, a^{3} b^{7} c^{7} d^{3} - 1470 \, a^{4} b^{6} c^{6} d^{4} + 2268 \, a^{5} b^{5} c^{5} d^{5} - 2310 \, a^{6} b^{4} c^{4} d^{6} + 1560 \, a^{7} b^{3} c^{3} d^{7} - 675 \, a^{8} b^{2} c^{2} d^{8} + 170 \, a^{9} b c d^{9} - 19 \, a^{10} d^{10} + 20 \, {\left (b^{10} c^{9} d - 9 \, a b^{9} c^{8} d^{2} + 36 \, a^{2} b^{8} c^{7} d^{3} - 84 \, a^{3} b^{7} c^{6} d^{4} + 126 \, a^{4} b^{6} c^{5} d^{5} - 126 \, a^{5} b^{5} c^{4} d^{6} + 84 \, a^{6} b^{4} c^{3} d^{7} - 36 \, a^{7} b^{3} c^{2} d^{8} + 9 \, a^{8} b^{2} c d^{9} - a^{9} b d^{10}\right )} x}{2 \, {\left (b^{13} x^{2} + 2 \, a b^{12} x + a^{2} b^{11}\right )}} + \frac {7 \, b^{7} d^{10} x^{8} + 8 \, {\left (10 \, b^{7} c d^{9} - 3 \, a b^{6} d^{10}\right )} x^{7} + 28 \, {\left (15 \, b^{7} c^{2} d^{8} - 10 \, a b^{6} c d^{9} + 2 \, a^{2} b^{5} d^{10}\right )} x^{6} + 56 \, {\left (24 \, b^{7} c^{3} d^{7} - 27 \, a b^{6} c^{2} d^{8} + 12 \, a^{2} b^{5} c d^{9} - 2 \, a^{3} b^{4} d^{10}\right )} x^{5} + 70 \, {\left (42 \, b^{7} c^{4} d^{6} - 72 \, a b^{6} c^{3} d^{7} + 54 \, a^{2} b^{5} c^{2} d^{8} - 20 \, a^{3} b^{4} c d^{9} + 3 \, a^{4} b^{3} d^{10}\right )} x^{4} + 56 \, {\left (84 \, b^{7} c^{5} d^{5} - 210 \, a b^{6} c^{4} d^{6} + 240 \, a^{2} b^{5} c^{3} d^{7} - 150 \, a^{3} b^{4} c^{2} d^{8} + 50 \, a^{4} b^{3} c d^{9} - 7 \, a^{5} b^{2} d^{10}\right )} x^{3} + 28 \, {\left (210 \, b^{7} c^{6} d^{4} - 756 \, a b^{6} c^{5} d^{5} + 1260 \, a^{2} b^{5} c^{4} d^{6} - 1200 \, a^{3} b^{4} c^{3} d^{7} + 675 \, a^{4} b^{3} c^{2} d^{8} - 210 \, a^{5} b^{2} c d^{9} + 28 \, a^{6} b d^{10}\right )} x^{2} + 56 \, {\left (120 \, b^{7} c^{7} d^{3} - 630 \, a b^{6} c^{6} d^{4} + 1512 \, a^{2} b^{5} c^{5} d^{5} - 2100 \, a^{3} b^{4} c^{4} d^{6} + 1800 \, a^{4} b^{3} c^{3} d^{7} - 945 \, a^{5} b^{2} c^{2} d^{8} + 280 \, a^{6} b c d^{9} - 36 \, a^{7} d^{10}\right )} x}{56 \, b^{10}} + \frac {45 \, {\left (b^{8} c^{8} d^{2} - 8 \, a b^{7} c^{7} d^{3} + 28 \, a^{2} b^{6} c^{6} d^{4} - 56 \, a^{3} b^{5} c^{5} d^{5} + 70 \, a^{4} b^{4} c^{4} d^{6} - 56 \, a^{5} b^{3} c^{3} d^{7} + 28 \, a^{6} b^{2} c^{2} d^{8} - 8 \, a^{7} b c d^{9} + a^{8} d^{10}\right )} \log \left (b x + a\right )}{b^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1233 vs.
\(2 (252) = 504\).
time = 0.30, size = 1233, normalized size = 4.71
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 843 vs.
\(2 (243) = 486\).
time = 6.30, size = 843, normalized size = 3.22 \begin {gather*} x^{7} \left (- \frac {3 a d^{10}}{7 b^{4}} + \frac {10 c d^{9}}{7 b^{3}}\right ) + x^{6} \left (\frac {a^{2} d^{10}}{b^{5}} - \frac {5 a c d^{9}}{b^{4}} + \frac {15 c^{2} d^{8}}{2 b^{3}}\right ) + x^{5} \left (- \frac {2 a^{3} d^{10}}{b^{6}} + \frac {12 a^{2} c d^{9}}{b^{5}} - \frac {27 a c^{2} d^{8}}{b^{4}} + \frac {24 c^{3} d^{7}}{b^{3}}\right ) + x^{4} \cdot \left (\frac {15 a^{4} d^{10}}{4 b^{7}} - \frac {25 a^{3} c d^{9}}{b^{6}} + \frac {135 a^{2} c^{2} d^{8}}{2 b^{5}} - \frac {90 a c^{3} d^{7}}{b^{4}} + \frac {105 c^{4} d^{6}}{2 b^{3}}\right ) + x^{3} \left (- \frac {7 a^{5} d^{10}}{b^{8}} + \frac {50 a^{4} c d^{9}}{b^{7}} - \frac {150 a^{3} c^{2} d^{8}}{b^{6}} + \frac {240 a^{2} c^{3} d^{7}}{b^{5}} - \frac {210 a c^{4} d^{6}}{b^{4}} + \frac {84 c^{5} d^{5}}{b^{3}}\right ) + x^{2} \cdot \left (\frac {14 a^{6} d^{10}}{b^{9}} - \frac {105 a^{5} c d^{9}}{b^{8}} + \frac {675 a^{4} c^{2} d^{8}}{2 b^{7}} - \frac {600 a^{3} c^{3} d^{7}}{b^{6}} + \frac {630 a^{2} c^{4} d^{6}}{b^{5}} - \frac {378 a c^{5} d^{5}}{b^{4}} + \frac {105 c^{6} d^{4}}{b^{3}}\right ) + x \left (- \frac {36 a^{7} d^{10}}{b^{10}} + \frac {280 a^{6} c d^{9}}{b^{9}} - \frac {945 a^{5} c^{2} d^{8}}{b^{8}} + \frac {1800 a^{4} c^{3} d^{7}}{b^{7}} - \frac {2100 a^{3} c^{4} d^{6}}{b^{6}} + \frac {1512 a^{2} c^{5} d^{5}}{b^{5}} - \frac {630 a c^{6} d^{4}}{b^{4}} + \frac {120 c^{7} d^{3}}{b^{3}}\right ) + \frac {19 a^{10} d^{10} - 170 a^{9} b c d^{9} + 675 a^{8} b^{2} c^{2} d^{8} - 1560 a^{7} b^{3} c^{3} d^{7} + 2310 a^{6} b^{4} c^{4} d^{6} - 2268 a^{5} b^{5} c^{5} d^{5} + 1470 a^{4} b^{6} c^{6} d^{4} - 600 a^{3} b^{7} c^{7} d^{3} + 135 a^{2} b^{8} c^{8} d^{2} - 10 a b^{9} c^{9} d - b^{10} c^{10} + x \left (20 a^{9} b d^{10} - 180 a^{8} b^{2} c d^{9} + 720 a^{7} b^{3} c^{2} d^{8} - 1680 a^{6} b^{4} c^{3} d^{7} + 2520 a^{5} b^{5} c^{4} d^{6} - 2520 a^{4} b^{6} c^{5} d^{5} + 1680 a^{3} b^{7} c^{6} d^{4} - 720 a^{2} b^{8} c^{7} d^{3} + 180 a b^{9} c^{8} d^{2} - 20 b^{10} c^{9} d\right )}{2 a^{2} b^{11} + 4 a b^{12} x + 2 b^{13} x^{2}} + \frac {d^{10} x^{8}}{8 b^{3}} + \frac {45 d^{2} \left (a d - b c\right )^{8} \log {\left (a + b x \right )}}{b^{11}} \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. 924 vs.
\(2 (252) = 504\).
time = 0.00, size = 976, normalized size = 3.73 \begin {gather*} \frac {\frac {1}{8} x^{8} d^{10} b^{21}-\frac {3}{7} x^{7} d^{10} b^{20} a+\frac {10}{7} x^{7} d^{9} c b^{21}+x^{6} d^{10} b^{19} a^{2}-5 x^{6} d^{9} c b^{20} a+\frac {15}{2} x^{6} d^{8} c^{2} b^{21}-2 x^{5} d^{10} b^{18} a^{3}+12 x^{5} d^{9} c b^{19} a^{2}-27 x^{5} d^{8} c^{2} b^{20} a+24 x^{5} d^{7} c^{3} b^{21}+\frac {15}{4} x^{4} d^{10} b^{17} a^{4}-25 x^{4} d^{9} c b^{18} a^{3}+\frac {135}{2} x^{4} d^{8} c^{2} b^{19} a^{2}-90 x^{4} d^{7} c^{3} b^{20} a+\frac {105}{2} x^{4} d^{6} c^{4} b^{21}-7 x^{3} d^{10} b^{16} a^{5}+50 x^{3} d^{9} c b^{17} a^{4}-150 x^{3} d^{8} c^{2} b^{18} a^{3}+240 x^{3} d^{7} c^{3} b^{19} a^{2}-210 x^{3} d^{6} c^{4} b^{20} a+84 x^{3} d^{5} c^{5} b^{21}+14 x^{2} d^{10} b^{15} a^{6}-105 x^{2} d^{9} c b^{16} a^{5}+\frac {675}{2} x^{2} d^{8} c^{2} b^{17} a^{4}-600 x^{2} d^{7} c^{3} b^{18} a^{3}+630 x^{2} d^{6} c^{4} b^{19} a^{2}-378 x^{2} d^{5} c^{5} b^{20} a+105 x^{2} d^{4} c^{6} b^{21}-36 x d^{10} b^{14} a^{7}+280 x d^{9} c b^{15} a^{6}-945 x d^{8} c^{2} b^{16} a^{5}+1800 x d^{7} c^{3} b^{17} a^{4}-2100 x d^{6} c^{4} b^{18} a^{3}+1512 x d^{5} c^{5} b^{19} a^{2}-630 x d^{4} c^{6} b^{20} a+120 x d^{3} c^{7} b^{21}}{b^{24}}+\frac {\frac {1}{2} \left (19 d^{10} a^{10}-170 d^{9} b a^{9} c+675 d^{8} b^{2} a^{8} c^{2}-1560 d^{7} b^{3} a^{7} c^{3}+2310 d^{6} b^{4} a^{6} c^{4}-2268 d^{5} b^{5} a^{5} c^{5}+1470 d^{4} b^{6} a^{4} c^{6}-600 d^{3} b^{7} a^{3} c^{7}+135 d^{2} b^{8} a^{2} c^{8}-10 d b^{9} a c^{9}-b^{10} c^{10}+\left (20 d^{10} b a^{9}-180 d^{9} b^{2} a^{8} c+720 d^{8} b^{3} a^{7} c^{2}-1680 d^{7} b^{4} a^{6} c^{3}+2520 d^{6} b^{5} a^{5} c^{4}-2520 d^{5} b^{6} a^{4} c^{5}+1680 d^{4} b^{7} a^{3} c^{6}-720 d^{3} b^{8} a^{2} c^{7}+180 d^{2} b^{9} a c^{8}-20 d b^{10} c^{9}\right ) x\right )}{b^{11} \left (x b+a\right )^{2}}+\frac {\left (45 d^{10} a^{8}-360 d^{9} c b a^{7}+1260 d^{8} c^{2} b^{2} a^{6}-2520 d^{7} c^{3} b^{3} a^{5}+3150 d^{6} c^{4} b^{4} a^{4}-2520 d^{5} c^{5} b^{5} a^{3}+1260 d^{4} c^{6} b^{6} a^{2}-360 d^{3} c^{7} b^{7} a+45 d^{2} c^{8} b^{8}\right ) \ln \left |x b+a\right |}{b^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.38, size = 3299, normalized size = 12.59
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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