Optimal. Leaf size=225 \[ \frac {(b c-a d)^8 (c+d x)^{11}}{11 d^9}-\frac {2 b (b c-a d)^7 (c+d x)^{12}}{3 d^9}+\frac {28 b^2 (b c-a d)^6 (c+d x)^{13}}{13 d^9}-\frac {4 b^3 (b c-a d)^5 (c+d x)^{14}}{d^9}+\frac {14 b^4 (b c-a d)^4 (c+d x)^{15}}{3 d^9}-\frac {7 b^5 (b c-a d)^3 (c+d x)^{16}}{2 d^9}+\frac {28 b^6 (b c-a d)^2 (c+d x)^{17}}{17 d^9}-\frac {4 b^7 (b c-a d) (c+d x)^{18}}{9 d^9}+\frac {b^8 (c+d x)^{19}}{19 d^9} \]
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Rubi [A]
time = 0.61, antiderivative size = 225, 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 {4 b^7 (c+d x)^{18} (b c-a d)}{9 d^9}+\frac {28 b^6 (c+d x)^{17} (b c-a d)^2}{17 d^9}-\frac {7 b^5 (c+d x)^{16} (b c-a d)^3}{2 d^9}+\frac {14 b^4 (c+d x)^{15} (b c-a d)^4}{3 d^9}-\frac {4 b^3 (c+d x)^{14} (b c-a d)^5}{d^9}+\frac {28 b^2 (c+d x)^{13} (b c-a d)^6}{13 d^9}-\frac {2 b (c+d x)^{12} (b c-a d)^7}{3 d^9}+\frac {(c+d x)^{11} (b c-a d)^8}{11 d^9}+\frac {b^8 (c+d x)^{19}}{19 d^9} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (a+b x)^8 (c+d x)^{10} \, dx &=\int \left (\frac {(-b c+a d)^8 (c+d x)^{10}}{d^8}-\frac {8 b (b c-a d)^7 (c+d x)^{11}}{d^8}+\frac {28 b^2 (b c-a d)^6 (c+d x)^{12}}{d^8}-\frac {56 b^3 (b c-a d)^5 (c+d x)^{13}}{d^8}+\frac {70 b^4 (b c-a d)^4 (c+d x)^{14}}{d^8}-\frac {56 b^5 (b c-a d)^3 (c+d x)^{15}}{d^8}+\frac {28 b^6 (b c-a d)^2 (c+d x)^{16}}{d^8}-\frac {8 b^7 (b c-a d) (c+d x)^{17}}{d^8}+\frac {b^8 (c+d x)^{18}}{d^8}\right ) \, dx\\ &=\frac {(b c-a d)^8 (c+d x)^{11}}{11 d^9}-\frac {2 b (b c-a d)^7 (c+d x)^{12}}{3 d^9}+\frac {28 b^2 (b c-a d)^6 (c+d x)^{13}}{13 d^9}-\frac {4 b^3 (b c-a d)^5 (c+d x)^{14}}{d^9}+\frac {14 b^4 (b c-a d)^4 (c+d x)^{15}}{3 d^9}-\frac {7 b^5 (b c-a d)^3 (c+d x)^{16}}{2 d^9}+\frac {28 b^6 (b c-a d)^2 (c+d x)^{17}}{17 d^9}-\frac {4 b^7 (b c-a d) (c+d x)^{18}}{9 d^9}+\frac {b^8 (c+d x)^{19}}{19 d^9}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1241\) vs. \(2(225)=450\).
time = 0.09, size = 1241, normalized size = 5.52 \begin {gather*} a^8 c^{10} x+a^7 c^9 (4 b c+5 a d) x^2+\frac {1}{3} a^6 c^8 \left (28 b^2 c^2+80 a b c d+45 a^2 d^2\right ) x^3+2 a^5 c^7 \left (7 b^3 c^3+35 a b^2 c^2 d+45 a^2 b c d^2+15 a^3 d^3\right ) x^4+2 a^4 c^6 \left (7 b^4 c^4+56 a b^3 c^3 d+126 a^2 b^2 c^2 d^2+96 a^3 b c d^3+21 a^4 d^4\right ) x^5+\frac {14}{3} a^3 c^5 \left (2 b^5 c^5+25 a b^4 c^4 d+90 a^2 b^3 c^3 d^2+120 a^3 b^2 c^2 d^3+60 a^4 b c d^4+9 a^5 d^5\right ) x^6+2 a^2 c^4 \left (2 b^6 c^6+40 a b^5 c^5 d+225 a^2 b^4 c^4 d^2+480 a^3 b^3 c^3 d^3+420 a^4 b^2 c^2 d^4+144 a^5 b c d^5+15 a^6 d^6\right ) x^7+a c^3 \left (b^7 c^7+35 a b^6 c^6 d+315 a^2 b^5 c^5 d^2+1050 a^3 b^4 c^4 d^3+1470 a^4 b^3 c^3 d^4+882 a^5 b^2 c^2 d^5+210 a^6 b c d^6+15 a^7 d^7\right ) x^8+\frac {1}{9} c^2 \left (b^8 c^8+80 a b^7 c^7 d+1260 a^2 b^6 c^6 d^2+6720 a^3 b^5 c^5 d^3+14700 a^4 b^4 c^4 d^4+14112 a^5 b^3 c^3 d^5+5880 a^6 b^2 c^2 d^6+960 a^7 b c d^7+45 a^8 d^8\right ) x^9+c d \left (b^8 c^8+36 a b^7 c^7 d+336 a^2 b^6 c^6 d^2+1176 a^3 b^5 c^5 d^3+1764 a^4 b^4 c^4 d^4+1176 a^5 b^3 c^3 d^5+336 a^6 b^2 c^2 d^6+36 a^7 b c d^7+a^8 d^8\right ) x^{10}+\frac {1}{11} d^2 \left (45 b^8 c^8+960 a b^7 c^7 d+5880 a^2 b^6 c^6 d^2+14112 a^3 b^5 c^5 d^3+14700 a^4 b^4 c^4 d^4+6720 a^5 b^3 c^3 d^5+1260 a^6 b^2 c^2 d^6+80 a^7 b c d^7+a^8 d^8\right ) x^{11}+\frac {2}{3} b d^3 \left (15 b^7 c^7+210 a b^6 c^6 d+882 a^2 b^5 c^5 d^2+1470 a^3 b^4 c^4 d^3+1050 a^4 b^3 c^3 d^4+315 a^5 b^2 c^2 d^5+35 a^6 b c d^6+a^7 d^7\right ) x^{12}+\frac {14}{13} b^2 d^4 \left (15 b^6 c^6+144 a b^5 c^5 d+420 a^2 b^4 c^4 d^2+480 a^3 b^3 c^3 d^3+225 a^4 b^2 c^2 d^4+40 a^5 b c d^5+2 a^6 d^6\right ) x^{13}+2 b^3 d^5 \left (9 b^5 c^5+60 a b^4 c^4 d+120 a^2 b^3 c^3 d^2+90 a^3 b^2 c^2 d^3+25 a^4 b c d^4+2 a^5 d^5\right ) x^{14}+\frac {2}{3} b^4 d^6 \left (21 b^4 c^4+96 a b^3 c^3 d+126 a^2 b^2 c^2 d^2+56 a^3 b c d^3+7 a^4 d^4\right ) x^{15}+\frac {1}{2} b^5 d^7 \left (15 b^3 c^3+45 a b^2 c^2 d+35 a^2 b c d^2+7 a^3 d^3\right ) x^{16}+\frac {1}{17} b^6 d^8 \left (45 b^2 c^2+80 a b c d+28 a^2 d^2\right ) x^{17}+\frac {1}{9} b^7 d^9 (5 b c+4 a d) x^{18}+\frac {1}{19} b^8 d^{10} x^{19} \end {gather*}
Antiderivative was successfully verified.
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Mathics [B] Leaf count is larger than twice the leaf count of optimal. \(1214\) vs. \(2(225)=450\).
time = 11.47, size = 1212, normalized size = 5.39 \begin {gather*} \frac {x \left (831402 a^8 c^{10}+831402 a^7 c^9 x \left (5 a d+4 b c\right )+a^6 c^8 x^2 \left (12471030 a^2 d^2+22170720 a b c d+7759752 b^2 c^2\right )+a^5 c^7 x^3 \left (24942060 a^3 d^3+74826180 a^2 b c d^2+58198140 a b^2 c^2 d+11639628 b^3 c^3\right )+a^4 c^6 x^4 \left (34918884 a^4 d^4+159629184 a^3 b c d^3+209513304 a^2 b^2 c^2 d^2+93117024 a b^3 c^3 d+11639628 b^4 c^4\right )+a^3 c^5 x^5 \left (34918884 a^5 d^5+232792560 a^4 b c d^4+465585120 a^3 b^2 c^2 d^3+349188840 a^2 b^3 c^3 d^2+96996900 a b^4 c^4 d+7759752 b^5 c^5\right )+a^2 c^4 x^6 \left (24942060 a^6 d^6+239443776 a^5 b c d^5+698377680 a^4 b^2 c^2 d^4+798145920 a^3 b^3 c^3 d^3+374130900 a^2 b^4 c^4 d^2+66512160 a b^5 c^5 d+3325608 b^6 c^6\right )+831402 a c^3 x^7 \left (15 a^7 d^7+210 a^6 b c d^6+882 a^5 b^2 c^2 d^5+1470 a^4 b^3 c^3 d^4+1050 a^3 b^4 c^4 d^3+315 a^2 b^5 c^5 d^2+35 a b^6 c^6 d+b^7 c^7\right )+554268 b d^3 x^{11} \left (a^7 d^7+35 a^6 b c d^6+315 a^5 b^2 c^2 d^5+1050 a^4 b^3 c^3 d^4+1470 a^3 b^4 c^4 d^3+882 a^2 b^5 c^5 d^2+210 a b^6 c^6 d+15 b^7 c^7\right )+b^5 d^7 x^{15} \left (2909907 a^3 d^3+14549535 a^2 b c d^2+18706545 a b^2 c^2 d+6235515 b^3 c^3\right )+b^7 d^9 x^{17} \left (369512 a d+461890 b c\right )+c^2 x^8 \left (4157010 a^8 d^8+88682880 a^7 b c d^7+543182640 a^6 b^2 c^2 d^6+1303638336 a^5 b^3 c^3 d^5+1357956600 a^4 b^4 c^4 d^4+620780160 a^3 b^5 c^5 d^3+116396280 a^2 b^6 c^6 d^2+7390240 a b^7 c^7 d+92378 b^8 c^8\right )+d^2 x^{10} \left (75582 a^8 d^8+6046560 a^7 b c d^7+95233320 a^6 b^2 c^2 d^6+507911040 a^5 b^3 c^3 d^5+1111055400 a^4 b^4 c^4 d^4+1066613184 a^3 b^5 c^5 d^3+444422160 a^2 b^6 c^6 d^2+72558720 a b^7 c^7 d+3401190 b^8 c^8\right )+b^2 d^4 x^{12} \left (1790712 a^6 d^6+35814240 a^5 b c d^5+201455100 a^4 b^2 c^2 d^4+429770880 a^3 b^3 c^3 d^3+376049520 a^2 b^4 c^4 d^2+128931264 a b^5 c^5 d+13430340 b^6 c^6\right )+b^3 d^5 x^{13} \left (3325608 a^5 d^5+41570100 a^4 b c d^4+149652360 a^3 b^2 c^2 d^3+199536480 a^2 b^3 c^3 d^2+99768240 a b^4 c^4 d+14965236 b^5 c^5\right )+b^4 d^6 x^{14} \left (3879876 a^4 d^4+31039008 a^3 b c d^3+69837768 a^2 b^2 c^2 d^2+53209728 a b^3 c^3 d+11639628 b^4 c^4\right )+b^6 d^8 x^{16} \left (1369368 a^2 d^2+3912480 a b c d+2200770 b^2 c^2\right )+43758 b^8 d^{10} x^{18}+831402 c d x^9 \left (a^8 d^8+36 a^7 b c d^7+336 a^6 b^2 c^2 d^6+1176 a^5 b^3 c^3 d^5+1764 a^4 b^4 c^4 d^4+1176 a^3 b^5 c^5 d^3+336 a^2 b^6 c^6 d^2+36 a b^7 c^7 d+b^8 c^8\right )\right )}{831402} \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. \(1290\) vs.
\(2(209)=418\).
time = 0.15, size = 1291, normalized size = 5.74
method | result | size |
norman | \(a^{8} c^{10} x +\left (5 a^{8} c^{9} d +4 a^{7} b \,c^{10}\right ) x^{2}+\left (15 a^{8} c^{8} d^{2}+\frac {80}{3} a^{7} b \,c^{9} d +\frac {28}{3} a^{6} b^{2} c^{10}\right ) x^{3}+\left (30 a^{8} c^{7} d^{3}+90 a^{7} b \,c^{8} d^{2}+70 a^{6} b^{2} c^{9} d +14 a^{5} b^{3} c^{10}\right ) x^{4}+\left (42 a^{8} c^{6} d^{4}+192 a^{7} b \,c^{7} d^{3}+252 a^{6} b^{2} c^{8} d^{2}+112 a^{5} b^{3} c^{9} d +14 a^{4} b^{4} c^{10}\right ) x^{5}+\left (42 a^{8} c^{5} d^{5}+280 a^{7} b \,c^{6} d^{4}+560 a^{6} b^{2} c^{7} d^{3}+420 a^{5} b^{3} c^{8} d^{2}+\frac {350}{3} a^{4} b^{4} c^{9} d +\frac {28}{3} a^{3} b^{5} c^{10}\right ) x^{6}+\left (30 a^{8} c^{4} d^{6}+288 a^{7} b \,c^{5} d^{5}+840 a^{6} b^{2} c^{6} d^{4}+960 a^{5} b^{3} c^{7} d^{3}+450 a^{4} b^{4} c^{8} d^{2}+80 a^{3} b^{5} c^{9} d +4 b^{6} a^{2} c^{10}\right ) x^{7}+\left (15 a^{8} c^{3} d^{7}+210 a^{7} b \,c^{4} d^{6}+882 a^{6} b^{2} c^{5} d^{5}+1470 a^{5} b^{3} c^{6} d^{4}+1050 a^{4} b^{4} c^{7} d^{3}+315 a^{3} b^{5} c^{8} d^{2}+35 b^{6} a^{2} c^{9} d +a \,b^{7} c^{10}\right ) x^{8}+\left (5 a^{8} c^{2} d^{8}+\frac {320}{3} a^{7} b \,c^{3} d^{7}+\frac {1960}{3} a^{6} b^{2} c^{4} d^{6}+1568 a^{5} b^{3} c^{5} d^{5}+\frac {4900}{3} a^{4} b^{4} c^{6} d^{4}+\frac {2240}{3} a^{3} b^{5} c^{7} d^{3}+140 b^{6} a^{2} c^{8} d^{2}+\frac {80}{9} a \,b^{7} c^{9} d +\frac {1}{9} b^{8} c^{10}\right ) x^{9}+\left (a^{8} c \,d^{9}+36 a^{7} b \,c^{2} d^{8}+336 a^{6} b^{2} c^{3} d^{7}+1176 a^{5} b^{3} c^{4} d^{6}+1764 a^{4} b^{4} c^{5} d^{5}+1176 a^{3} b^{5} c^{6} d^{4}+336 b^{6} a^{2} c^{7} d^{3}+36 a \,b^{7} c^{8} d^{2}+b^{8} c^{9} d \right ) x^{10}+\left (\frac {1}{11} a^{8} d^{10}+\frac {80}{11} a^{7} b c \,d^{9}+\frac {1260}{11} a^{6} b^{2} c^{2} d^{8}+\frac {6720}{11} a^{5} b^{3} c^{3} d^{7}+\frac {14700}{11} a^{4} b^{4} c^{4} d^{6}+\frac {14112}{11} a^{3} b^{5} c^{5} d^{5}+\frac {5880}{11} b^{6} a^{2} c^{6} d^{4}+\frac {960}{11} a \,b^{7} c^{7} d^{3}+\frac {45}{11} b^{8} c^{8} d^{2}\right ) x^{11}+\left (\frac {2}{3} a^{7} b \,d^{10}+\frac {70}{3} a^{6} b^{2} c \,d^{9}+210 a^{5} b^{3} c^{2} d^{8}+700 a^{4} b^{4} c^{3} d^{7}+980 a^{3} b^{5} c^{4} d^{6}+588 b^{6} a^{2} c^{5} d^{5}+140 a \,b^{7} c^{6} d^{4}+10 b^{8} c^{7} d^{3}\right ) x^{12}+\left (\frac {28}{13} a^{6} b^{2} d^{10}+\frac {560}{13} a^{5} b^{3} c \,d^{9}+\frac {3150}{13} a^{4} b^{4} c^{2} d^{8}+\frac {6720}{13} a^{3} b^{5} c^{3} d^{7}+\frac {5880}{13} b^{6} a^{2} c^{4} d^{6}+\frac {2016}{13} a \,b^{7} c^{5} d^{5}+\frac {210}{13} b^{8} c^{6} d^{4}\right ) x^{13}+\left (4 a^{5} b^{3} d^{10}+50 a^{4} b^{4} c \,d^{9}+180 a^{3} b^{5} c^{2} d^{8}+240 b^{6} a^{2} c^{3} d^{7}+120 a \,b^{7} c^{4} d^{6}+18 b^{8} c^{5} d^{5}\right ) x^{14}+\left (\frac {14}{3} a^{4} b^{4} d^{10}+\frac {112}{3} a^{3} b^{5} c \,d^{9}+84 b^{6} a^{2} c^{2} d^{8}+64 a \,b^{7} c^{3} d^{7}+14 b^{8} c^{4} d^{6}\right ) x^{15}+\left (\frac {7}{2} a^{3} b^{5} d^{10}+\frac {35}{2} b^{6} a^{2} c \,d^{9}+\frac {45}{2} a \,b^{7} c^{2} d^{8}+\frac {15}{2} b^{8} c^{3} d^{7}\right ) x^{16}+\left (\frac {28}{17} b^{6} a^{2} d^{10}+\frac {80}{17} a \,b^{7} c \,d^{9}+\frac {45}{17} b^{8} c^{2} d^{8}\right ) x^{17}+\left (\frac {4}{9} a \,b^{7} d^{10}+\frac {5}{9} b^{8} c \,d^{9}\right ) x^{18}+\frac {b^{8} d^{10} x^{19}}{19}\) | \(1273\) |
default | \(\frac {b^{8} d^{10} x^{19}}{19}+\frac {\left (8 a \,b^{7} d^{10}+10 b^{8} c \,d^{9}\right ) x^{18}}{18}+\frac {\left (28 b^{6} a^{2} d^{10}+80 a \,b^{7} c \,d^{9}+45 b^{8} c^{2} d^{8}\right ) x^{17}}{17}+\frac {\left (56 a^{3} b^{5} d^{10}+280 b^{6} a^{2} c \,d^{9}+360 a \,b^{7} c^{2} d^{8}+120 b^{8} c^{3} d^{7}\right ) x^{16}}{16}+\frac {\left (70 a^{4} b^{4} d^{10}+560 a^{3} b^{5} c \,d^{9}+1260 b^{6} a^{2} c^{2} d^{8}+960 a \,b^{7} c^{3} d^{7}+210 b^{8} c^{4} d^{6}\right ) x^{15}}{15}+\frac {\left (56 a^{5} b^{3} d^{10}+700 a^{4} b^{4} c \,d^{9}+2520 a^{3} b^{5} c^{2} d^{8}+3360 b^{6} a^{2} c^{3} d^{7}+1680 a \,b^{7} c^{4} d^{6}+252 b^{8} c^{5} d^{5}\right ) x^{14}}{14}+\frac {\left (28 a^{6} b^{2} d^{10}+560 a^{5} b^{3} c \,d^{9}+3150 a^{4} b^{4} c^{2} d^{8}+6720 a^{3} b^{5} c^{3} d^{7}+5880 b^{6} a^{2} c^{4} d^{6}+2016 a \,b^{7} c^{5} d^{5}+210 b^{8} c^{6} d^{4}\right ) x^{13}}{13}+\frac {\left (8 a^{7} b \,d^{10}+280 a^{6} b^{2} c \,d^{9}+2520 a^{5} b^{3} c^{2} d^{8}+8400 a^{4} b^{4} c^{3} d^{7}+11760 a^{3} b^{5} c^{4} d^{6}+7056 b^{6} a^{2} c^{5} d^{5}+1680 a \,b^{7} c^{6} d^{4}+120 b^{8} c^{7} d^{3}\right ) x^{12}}{12}+\frac {\left (a^{8} d^{10}+80 a^{7} b c \,d^{9}+1260 a^{6} b^{2} c^{2} d^{8}+6720 a^{5} b^{3} c^{3} d^{7}+14700 a^{4} b^{4} c^{4} d^{6}+14112 a^{3} b^{5} c^{5} d^{5}+5880 b^{6} a^{2} c^{6} d^{4}+960 a \,b^{7} c^{7} d^{3}+45 b^{8} c^{8} d^{2}\right ) x^{11}}{11}+\frac {\left (10 a^{8} c \,d^{9}+360 a^{7} b \,c^{2} d^{8}+3360 a^{6} b^{2} c^{3} d^{7}+11760 a^{5} b^{3} c^{4} d^{6}+17640 a^{4} b^{4} c^{5} d^{5}+11760 a^{3} b^{5} c^{6} d^{4}+3360 b^{6} a^{2} c^{7} d^{3}+360 a \,b^{7} c^{8} d^{2}+10 b^{8} c^{9} d \right ) x^{10}}{10}+\frac {\left (45 a^{8} c^{2} d^{8}+960 a^{7} b \,c^{3} d^{7}+5880 a^{6} b^{2} c^{4} d^{6}+14112 a^{5} b^{3} c^{5} d^{5}+14700 a^{4} b^{4} c^{6} d^{4}+6720 a^{3} b^{5} c^{7} d^{3}+1260 b^{6} a^{2} c^{8} d^{2}+80 a \,b^{7} c^{9} d +b^{8} c^{10}\right ) x^{9}}{9}+\frac {\left (120 a^{8} c^{3} d^{7}+1680 a^{7} b \,c^{4} d^{6}+7056 a^{6} b^{2} c^{5} d^{5}+11760 a^{5} b^{3} c^{6} d^{4}+8400 a^{4} b^{4} c^{7} d^{3}+2520 a^{3} b^{5} c^{8} d^{2}+280 b^{6} a^{2} c^{9} d +8 a \,b^{7} c^{10}\right ) x^{8}}{8}+\frac {\left (210 a^{8} c^{4} d^{6}+2016 a^{7} b \,c^{5} d^{5}+5880 a^{6} b^{2} c^{6} d^{4}+6720 a^{5} b^{3} c^{7} d^{3}+3150 a^{4} b^{4} c^{8} d^{2}+560 a^{3} b^{5} c^{9} d +28 b^{6} a^{2} c^{10}\right ) x^{7}}{7}+\frac {\left (252 a^{8} c^{5} d^{5}+1680 a^{7} b \,c^{6} d^{4}+3360 a^{6} b^{2} c^{7} d^{3}+2520 a^{5} b^{3} c^{8} d^{2}+700 a^{4} b^{4} c^{9} d +56 a^{3} b^{5} c^{10}\right ) x^{6}}{6}+\frac {\left (210 a^{8} c^{6} d^{4}+960 a^{7} b \,c^{7} d^{3}+1260 a^{6} b^{2} c^{8} d^{2}+560 a^{5} b^{3} c^{9} d +70 a^{4} b^{4} c^{10}\right ) x^{5}}{5}+\frac {\left (120 a^{8} c^{7} d^{3}+360 a^{7} b \,c^{8} d^{2}+280 a^{6} b^{2} c^{9} d +56 a^{5} b^{3} c^{10}\right ) x^{4}}{4}+\frac {\left (45 a^{8} c^{8} d^{2}+80 a^{7} b \,c^{9} d +28 a^{6} b^{2} c^{10}\right ) x^{3}}{3}+\frac {\left (10 a^{8} c^{9} d +8 a^{7} b \,c^{10}\right ) x^{2}}{2}+a^{8} c^{10} x\) | \(1291\) |
gosper | \(\frac {2}{3} x^{12} a^{7} b \,d^{10}+10 x^{12} b^{8} c^{7} d^{3}+\frac {28}{13} x^{13} a^{6} b^{2} d^{10}+\frac {210}{13} x^{13} b^{8} c^{6} d^{4}+\frac {14}{3} x^{15} a^{4} b^{4} d^{10}+14 x^{15} b^{8} c^{4} d^{6}+\frac {7}{2} x^{16} a^{3} b^{5} d^{10}+\frac {15}{2} x^{16} b^{8} c^{3} d^{7}+\frac {28}{17} x^{17} b^{6} a^{2} d^{10}+\frac {45}{17} x^{17} b^{8} c^{2} d^{8}+\frac {4}{9} x^{18} a \,b^{7} d^{10}+15 x^{3} a^{8} c^{8} d^{2}+\frac {28}{3} x^{3} a^{6} b^{2} c^{10}+42 x^{6} a^{8} c^{5} d^{5}+\frac {28}{3} x^{6} a^{3} b^{5} c^{10}+5 x^{9} a^{8} c^{2} d^{8}+\frac {45}{11} x^{11} b^{8} c^{8} d^{2}+14 a^{4} b^{4} c^{10} x^{5}+30 a^{8} c^{4} d^{6} x^{7}+4 a^{2} b^{6} c^{10} x^{7}+15 a^{8} c^{3} d^{7} x^{8}+a \,b^{7} c^{10} x^{8}+\frac {5}{9} x^{18} b^{8} c \,d^{9}+5 a^{8} c^{9} d \,x^{2}+4 a^{7} b \,c^{10} x^{2}+30 a^{8} c^{7} d^{3} x^{4}+14 a^{5} b^{3} c^{10} x^{4}+42 a^{8} c^{6} d^{4} x^{5}+a^{8} c^{10} x +\frac {1}{19} b^{8} d^{10} x^{19}+\frac {1}{9} x^{9} b^{8} c^{10}+\frac {1}{11} x^{11} a^{8} d^{10}+120 a \,b^{7} c^{4} d^{6} x^{14}+210 a^{7} b \,c^{4} d^{6} x^{8}+882 a^{6} b^{2} c^{5} d^{5} x^{8}+1470 a^{5} b^{3} c^{6} d^{4} x^{8}+1050 a^{4} b^{4} c^{7} d^{3} x^{8}+315 a^{3} b^{5} c^{8} d^{2} x^{8}+35 a^{2} b^{6} c^{9} d \,x^{8}+36 a^{7} b \,c^{2} d^{8} x^{10}+336 a^{6} b^{2} c^{3} d^{7} x^{10}+1176 a^{5} b^{3} c^{4} d^{6} x^{10}+1764 a^{4} b^{4} c^{5} d^{5} x^{10}+1176 a^{3} b^{5} c^{6} d^{4} x^{10}+336 a^{2} b^{6} c^{7} d^{3} x^{10}+36 a \,b^{7} c^{8} d^{2} x^{10}+50 a^{4} b^{4} c \,d^{9} x^{14}+180 a^{3} b^{5} c^{2} d^{8} x^{14}+240 a^{2} b^{6} c^{3} d^{7} x^{14}+70 a^{6} b^{2} c^{9} d \,x^{4}+192 a^{7} b \,c^{7} d^{3} x^{5}+252 a^{6} b^{2} c^{8} d^{2} x^{5}+112 a^{5} b^{3} c^{9} d \,x^{5}+288 a^{7} b \,c^{5} d^{5} x^{7}+840 a^{6} b^{2} c^{6} d^{4} x^{7}+960 a^{5} b^{3} c^{7} d^{3} x^{7}+450 a^{4} b^{4} c^{8} d^{2} x^{7}+80 a^{3} b^{5} c^{9} d \,x^{7}+84 x^{15} b^{6} a^{2} c^{2} d^{8}+64 x^{15} a \,b^{7} c^{3} d^{7}+\frac {35}{2} x^{16} b^{6} a^{2} c \,d^{9}+\frac {45}{2} x^{16} a \,b^{7} c^{2} d^{8}+\frac {80}{17} x^{17} a \,b^{7} c \,d^{9}+90 a^{7} b \,c^{8} d^{2} x^{4}+980 x^{12} a^{3} b^{5} c^{4} d^{6}+588 x^{12} b^{6} a^{2} c^{5} d^{5}+140 x^{12} a \,b^{7} c^{6} d^{4}+\frac {560}{13} x^{13} a^{5} b^{3} c \,d^{9}+\frac {3150}{13} x^{13} a^{4} b^{4} c^{2} d^{8}+\frac {6720}{13} x^{13} a^{3} b^{5} c^{3} d^{7}+\frac {5880}{13} x^{13} b^{6} a^{2} c^{4} d^{6}+\frac {2016}{13} x^{13} a \,b^{7} c^{5} d^{5}+\frac {112}{3} x^{15} a^{3} b^{5} c \,d^{9}+700 x^{12} a^{4} b^{4} c^{3} d^{7}+\frac {5880}{11} x^{11} b^{6} a^{2} c^{6} d^{4}+\frac {960}{11} x^{11} a \,b^{7} c^{7} d^{3}+\frac {70}{3} x^{12} a^{6} b^{2} c \,d^{9}+210 x^{12} a^{5} b^{3} c^{2} d^{8}+\frac {1960}{3} x^{9} a^{6} b^{2} c^{4} d^{6}+1568 x^{9} a^{5} b^{3} c^{5} d^{5}+\frac {4900}{3} x^{9} a^{4} b^{4} c^{6} d^{4}+\frac {2240}{3} x^{9} a^{3} b^{5} c^{7} d^{3}+140 x^{9} b^{6} a^{2} c^{8} d^{2}+\frac {80}{9} x^{9} a \,b^{7} c^{9} d +\frac {80}{11} x^{11} a^{7} b c \,d^{9}+\frac {1260}{11} x^{11} a^{6} b^{2} c^{2} d^{8}+\frac {6720}{11} x^{11} a^{5} b^{3} c^{3} d^{7}+\frac {14700}{11} x^{11} a^{4} b^{4} c^{4} d^{6}+\frac {14112}{11} x^{11} a^{3} b^{5} c^{5} d^{5}+\frac {350}{3} x^{6} a^{4} b^{4} c^{9} d +\frac {320}{3} x^{9} a^{7} b \,c^{3} d^{7}+\frac {80}{3} x^{3} a^{7} b \,c^{9} d +280 x^{6} a^{7} b \,c^{6} d^{4}+560 x^{6} a^{6} b^{2} c^{7} d^{3}+420 x^{6} a^{5} b^{3} c^{8} d^{2}+a^{8} c \,d^{9} x^{10}+b^{8} c^{9} d \,x^{10}+4 a^{5} b^{3} d^{10} x^{14}+18 b^{8} c^{5} d^{5} x^{14}\) | \(1479\) |
risch | \(\frac {2}{3} x^{12} a^{7} b \,d^{10}+10 x^{12} b^{8} c^{7} d^{3}+\frac {28}{13} x^{13} a^{6} b^{2} d^{10}+\frac {210}{13} x^{13} b^{8} c^{6} d^{4}+\frac {14}{3} x^{15} a^{4} b^{4} d^{10}+14 x^{15} b^{8} c^{4} d^{6}+\frac {7}{2} x^{16} a^{3} b^{5} d^{10}+\frac {15}{2} x^{16} b^{8} c^{3} d^{7}+\frac {28}{17} x^{17} b^{6} a^{2} d^{10}+\frac {45}{17} x^{17} b^{8} c^{2} d^{8}+\frac {4}{9} x^{18} a \,b^{7} d^{10}+15 x^{3} a^{8} c^{8} d^{2}+\frac {28}{3} x^{3} a^{6} b^{2} c^{10}+42 x^{6} a^{8} c^{5} d^{5}+\frac {28}{3} x^{6} a^{3} b^{5} c^{10}+5 x^{9} a^{8} c^{2} d^{8}+\frac {45}{11} x^{11} b^{8} c^{8} d^{2}+14 a^{4} b^{4} c^{10} x^{5}+30 a^{8} c^{4} d^{6} x^{7}+4 a^{2} b^{6} c^{10} x^{7}+15 a^{8} c^{3} d^{7} x^{8}+a \,b^{7} c^{10} x^{8}+\frac {5}{9} x^{18} b^{8} c \,d^{9}+5 a^{8} c^{9} d \,x^{2}+4 a^{7} b \,c^{10} x^{2}+30 a^{8} c^{7} d^{3} x^{4}+14 a^{5} b^{3} c^{10} x^{4}+42 a^{8} c^{6} d^{4} x^{5}+a^{8} c^{10} x +\frac {1}{19} b^{8} d^{10} x^{19}+\frac {1}{9} x^{9} b^{8} c^{10}+\frac {1}{11} x^{11} a^{8} d^{10}+120 a \,b^{7} c^{4} d^{6} x^{14}+210 a^{7} b \,c^{4} d^{6} x^{8}+882 a^{6} b^{2} c^{5} d^{5} x^{8}+1470 a^{5} b^{3} c^{6} d^{4} x^{8}+1050 a^{4} b^{4} c^{7} d^{3} x^{8}+315 a^{3} b^{5} c^{8} d^{2} x^{8}+35 a^{2} b^{6} c^{9} d \,x^{8}+36 a^{7} b \,c^{2} d^{8} x^{10}+336 a^{6} b^{2} c^{3} d^{7} x^{10}+1176 a^{5} b^{3} c^{4} d^{6} x^{10}+1764 a^{4} b^{4} c^{5} d^{5} x^{10}+1176 a^{3} b^{5} c^{6} d^{4} x^{10}+336 a^{2} b^{6} c^{7} d^{3} x^{10}+36 a \,b^{7} c^{8} d^{2} x^{10}+50 a^{4} b^{4} c \,d^{9} x^{14}+180 a^{3} b^{5} c^{2} d^{8} x^{14}+240 a^{2} b^{6} c^{3} d^{7} x^{14}+70 a^{6} b^{2} c^{9} d \,x^{4}+192 a^{7} b \,c^{7} d^{3} x^{5}+252 a^{6} b^{2} c^{8} d^{2} x^{5}+112 a^{5} b^{3} c^{9} d \,x^{5}+288 a^{7} b \,c^{5} d^{5} x^{7}+840 a^{6} b^{2} c^{6} d^{4} x^{7}+960 a^{5} b^{3} c^{7} d^{3} x^{7}+450 a^{4} b^{4} c^{8} d^{2} x^{7}+80 a^{3} b^{5} c^{9} d \,x^{7}+84 x^{15} b^{6} a^{2} c^{2} d^{8}+64 x^{15} a \,b^{7} c^{3} d^{7}+\frac {35}{2} x^{16} b^{6} a^{2} c \,d^{9}+\frac {45}{2} x^{16} a \,b^{7} c^{2} d^{8}+\frac {80}{17} x^{17} a \,b^{7} c \,d^{9}+90 a^{7} b \,c^{8} d^{2} x^{4}+980 x^{12} a^{3} b^{5} c^{4} d^{6}+588 x^{12} b^{6} a^{2} c^{5} d^{5}+140 x^{12} a \,b^{7} c^{6} d^{4}+\frac {560}{13} x^{13} a^{5} b^{3} c \,d^{9}+\frac {3150}{13} x^{13} a^{4} b^{4} c^{2} d^{8}+\frac {6720}{13} x^{13} a^{3} b^{5} c^{3} d^{7}+\frac {5880}{13} x^{13} b^{6} a^{2} c^{4} d^{6}+\frac {2016}{13} x^{13} a \,b^{7} c^{5} d^{5}+\frac {112}{3} x^{15} a^{3} b^{5} c \,d^{9}+700 x^{12} a^{4} b^{4} c^{3} d^{7}+\frac {5880}{11} x^{11} b^{6} a^{2} c^{6} d^{4}+\frac {960}{11} x^{11} a \,b^{7} c^{7} d^{3}+\frac {70}{3} x^{12} a^{6} b^{2} c \,d^{9}+210 x^{12} a^{5} b^{3} c^{2} d^{8}+\frac {1960}{3} x^{9} a^{6} b^{2} c^{4} d^{6}+1568 x^{9} a^{5} b^{3} c^{5} d^{5}+\frac {4900}{3} x^{9} a^{4} b^{4} c^{6} d^{4}+\frac {2240}{3} x^{9} a^{3} b^{5} c^{7} d^{3}+140 x^{9} b^{6} a^{2} c^{8} d^{2}+\frac {80}{9} x^{9} a \,b^{7} c^{9} d +\frac {80}{11} x^{11} a^{7} b c \,d^{9}+\frac {1260}{11} x^{11} a^{6} b^{2} c^{2} d^{8}+\frac {6720}{11} x^{11} a^{5} b^{3} c^{3} d^{7}+\frac {14700}{11} x^{11} a^{4} b^{4} c^{4} d^{6}+\frac {14112}{11} x^{11} a^{3} b^{5} c^{5} d^{5}+\frac {350}{3} x^{6} a^{4} b^{4} c^{9} d +\frac {320}{3} x^{9} a^{7} b \,c^{3} d^{7}+\frac {80}{3} x^{3} a^{7} b \,c^{9} d +280 x^{6} a^{7} b \,c^{6} d^{4}+560 x^{6} a^{6} b^{2} c^{7} d^{3}+420 x^{6} a^{5} b^{3} c^{8} d^{2}+a^{8} c \,d^{9} x^{10}+b^{8} c^{9} d \,x^{10}+4 a^{5} b^{3} d^{10} x^{14}+18 b^{8} c^{5} d^{5} x^{14}\) | \(1479\) |
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. 1283 vs.
\(2 (209) = 418\).
time = 0.29, size = 1283, normalized size = 5.70
result too large to display
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. 1283 vs.
\(2 (209) = 418\).
time = 0.29, size = 1283, normalized size = 5.70
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. 1428 vs.
\(2 (207) = 414\).
time = 0.13, size = 1428, normalized size = 6.35
result too large to display
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. 1478 vs.
\(2 (209) = 418\).
time = 0.00, size = 1558, normalized size = 6.92
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.71, size = 1253, normalized size = 5.57 \begin {gather*} x^7\,\left (30\,a^8\,c^4\,d^6+288\,a^7\,b\,c^5\,d^5+840\,a^6\,b^2\,c^6\,d^4+960\,a^5\,b^3\,c^7\,d^3+450\,a^4\,b^4\,c^8\,d^2+80\,a^3\,b^5\,c^9\,d+4\,a^2\,b^6\,c^{10}\right )+x^{13}\,\left (\frac {28\,a^6\,b^2\,d^{10}}{13}+\frac {560\,a^5\,b^3\,c\,d^9}{13}+\frac {3150\,a^4\,b^4\,c^2\,d^8}{13}+\frac {6720\,a^3\,b^5\,c^3\,d^7}{13}+\frac {5880\,a^2\,b^6\,c^4\,d^6}{13}+\frac {2016\,a\,b^7\,c^5\,d^5}{13}+\frac {210\,b^8\,c^6\,d^4}{13}\right )+x^8\,\left (15\,a^8\,c^3\,d^7+210\,a^7\,b\,c^4\,d^6+882\,a^6\,b^2\,c^5\,d^5+1470\,a^5\,b^3\,c^6\,d^4+1050\,a^4\,b^4\,c^7\,d^3+315\,a^3\,b^5\,c^8\,d^2+35\,a^2\,b^6\,c^9\,d+a\,b^7\,c^{10}\right )+x^{12}\,\left (\frac {2\,a^7\,b\,d^{10}}{3}+\frac {70\,a^6\,b^2\,c\,d^9}{3}+210\,a^5\,b^3\,c^2\,d^8+700\,a^4\,b^4\,c^3\,d^7+980\,a^3\,b^5\,c^4\,d^6+588\,a^2\,b^6\,c^5\,d^5+140\,a\,b^7\,c^6\,d^4+10\,b^8\,c^7\,d^3\right )+x^{10}\,\left (a^8\,c\,d^9+36\,a^7\,b\,c^2\,d^8+336\,a^6\,b^2\,c^3\,d^7+1176\,a^5\,b^3\,c^4\,d^6+1764\,a^4\,b^4\,c^5\,d^5+1176\,a^3\,b^5\,c^6\,d^4+336\,a^2\,b^6\,c^7\,d^3+36\,a\,b^7\,c^8\,d^2+b^8\,c^9\,d\right )+x^5\,\left (42\,a^8\,c^6\,d^4+192\,a^7\,b\,c^7\,d^3+252\,a^6\,b^2\,c^8\,d^2+112\,a^5\,b^3\,c^9\,d+14\,a^4\,b^4\,c^{10}\right )+x^{15}\,\left (\frac {14\,a^4\,b^4\,d^{10}}{3}+\frac {112\,a^3\,b^5\,c\,d^9}{3}+84\,a^2\,b^6\,c^2\,d^8+64\,a\,b^7\,c^3\,d^7+14\,b^8\,c^4\,d^6\right )+x^6\,\left (42\,a^8\,c^5\,d^5+280\,a^7\,b\,c^6\,d^4+560\,a^6\,b^2\,c^7\,d^3+420\,a^5\,b^3\,c^8\,d^2+\frac {350\,a^4\,b^4\,c^9\,d}{3}+\frac {28\,a^3\,b^5\,c^{10}}{3}\right )+x^{14}\,\left (4\,a^5\,b^3\,d^{10}+50\,a^4\,b^4\,c\,d^9+180\,a^3\,b^5\,c^2\,d^8+240\,a^2\,b^6\,c^3\,d^7+120\,a\,b^7\,c^4\,d^6+18\,b^8\,c^5\,d^5\right )+x^9\,\left (5\,a^8\,c^2\,d^8+\frac {320\,a^7\,b\,c^3\,d^7}{3}+\frac {1960\,a^6\,b^2\,c^4\,d^6}{3}+1568\,a^5\,b^3\,c^5\,d^5+\frac {4900\,a^4\,b^4\,c^6\,d^4}{3}+\frac {2240\,a^3\,b^5\,c^7\,d^3}{3}+140\,a^2\,b^6\,c^8\,d^2+\frac {80\,a\,b^7\,c^9\,d}{9}+\frac {b^8\,c^{10}}{9}\right )+x^{11}\,\left (\frac {a^8\,d^{10}}{11}+\frac {80\,a^7\,b\,c\,d^9}{11}+\frac {1260\,a^6\,b^2\,c^2\,d^8}{11}+\frac {6720\,a^5\,b^3\,c^3\,d^7}{11}+\frac {14700\,a^4\,b^4\,c^4\,d^6}{11}+\frac {14112\,a^3\,b^5\,c^5\,d^5}{11}+\frac {5880\,a^2\,b^6\,c^6\,d^4}{11}+\frac {960\,a\,b^7\,c^7\,d^3}{11}+\frac {45\,b^8\,c^8\,d^2}{11}\right )+a^8\,c^{10}\,x+\frac {b^8\,d^{10}\,x^{19}}{19}+2\,a^5\,c^7\,x^4\,\left (15\,a^3\,d^3+45\,a^2\,b\,c\,d^2+35\,a\,b^2\,c^2\,d+7\,b^3\,c^3\right )+\frac {b^5\,d^7\,x^{16}\,\left (7\,a^3\,d^3+35\,a^2\,b\,c\,d^2+45\,a\,b^2\,c^2\,d+15\,b^3\,c^3\right )}{2}+a^7\,c^9\,x^2\,\left (5\,a\,d+4\,b\,c\right )+\frac {b^7\,d^9\,x^{18}\,\left (4\,a\,d+5\,b\,c\right )}{9}+\frac {a^6\,c^8\,x^3\,\left (45\,a^2\,d^2+80\,a\,b\,c\,d+28\,b^2\,c^2\right )}{3}+\frac {b^6\,d^8\,x^{17}\,\left (28\,a^2\,d^2+80\,a\,b\,c\,d+45\,b^2\,c^2\right )}{17} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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