Optimal. Leaf size=250 \[ -\frac {(b c-a d)^9 (c+d x)^{11}}{11 d^{10}}+\frac {3 b (b c-a d)^8 (c+d x)^{12}}{4 d^{10}}-\frac {36 b^2 (b c-a d)^7 (c+d x)^{13}}{13 d^{10}}+\frac {6 b^3 (b c-a d)^6 (c+d x)^{14}}{d^{10}}-\frac {42 b^4 (b c-a d)^5 (c+d x)^{15}}{5 d^{10}}+\frac {63 b^5 (b c-a d)^4 (c+d x)^{16}}{8 d^{10}}-\frac {84 b^6 (b c-a d)^3 (c+d x)^{17}}{17 d^{10}}+\frac {2 b^7 (b c-a d)^2 (c+d x)^{18}}{d^{10}}-\frac {9 b^8 (b c-a d) (c+d x)^{19}}{19 d^{10}}+\frac {b^9 (c+d x)^{20}}{20 d^{10}} \]
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Rubi [A]
time = 0.93, antiderivative size = 250, 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 {9 b^8 (c+d x)^{19} (b c-a d)}{19 d^{10}}+\frac {2 b^7 (c+d x)^{18} (b c-a d)^2}{d^{10}}-\frac {84 b^6 (c+d x)^{17} (b c-a d)^3}{17 d^{10}}+\frac {63 b^5 (c+d x)^{16} (b c-a d)^4}{8 d^{10}}-\frac {42 b^4 (c+d x)^{15} (b c-a d)^5}{5 d^{10}}+\frac {6 b^3 (c+d x)^{14} (b c-a d)^6}{d^{10}}-\frac {36 b^2 (c+d x)^{13} (b c-a d)^7}{13 d^{10}}+\frac {3 b (c+d x)^{12} (b c-a d)^8}{4 d^{10}}-\frac {(c+d x)^{11} (b c-a d)^9}{11 d^{10}}+\frac {b^9 (c+d x)^{20}}{20 d^{10}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (a+b x)^9 (c+d x)^{10} \, dx &=\int \left (\frac {(-b c+a d)^9 (c+d x)^{10}}{d^9}+\frac {9 b (b c-a d)^8 (c+d x)^{11}}{d^9}-\frac {36 b^2 (b c-a d)^7 (c+d x)^{12}}{d^9}+\frac {84 b^3 (b c-a d)^6 (c+d x)^{13}}{d^9}-\frac {126 b^4 (b c-a d)^5 (c+d x)^{14}}{d^9}+\frac {126 b^5 (b c-a d)^4 (c+d x)^{15}}{d^9}-\frac {84 b^6 (b c-a d)^3 (c+d x)^{16}}{d^9}+\frac {36 b^7 (b c-a d)^2 (c+d x)^{17}}{d^9}-\frac {9 b^8 (b c-a d) (c+d x)^{18}}{d^9}+\frac {b^9 (c+d x)^{19}}{d^9}\right ) \, dx\\ &=-\frac {(b c-a d)^9 (c+d x)^{11}}{11 d^{10}}+\frac {3 b (b c-a d)^8 (c+d x)^{12}}{4 d^{10}}-\frac {36 b^2 (b c-a d)^7 (c+d x)^{13}}{13 d^{10}}+\frac {6 b^3 (b c-a d)^6 (c+d x)^{14}}{d^{10}}-\frac {42 b^4 (b c-a d)^5 (c+d x)^{15}}{5 d^{10}}+\frac {63 b^5 (b c-a d)^4 (c+d x)^{16}}{8 d^{10}}-\frac {84 b^6 (b c-a d)^3 (c+d x)^{17}}{17 d^{10}}+\frac {2 b^7 (b c-a d)^2 (c+d x)^{18}}{d^{10}}-\frac {9 b^8 (b c-a d) (c+d x)^{19}}{19 d^{10}}+\frac {b^9 (c+d x)^{20}}{20 d^{10}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1397\) vs. \(2(250)=500\).
time = 0.12, size = 1397, normalized size = 5.59 \begin {gather*} a^9 c^{10} x+\frac {1}{2} a^8 c^9 (9 b c+10 a d) x^2+3 a^7 c^8 \left (4 b^2 c^2+10 a b c d+5 a^2 d^2\right ) x^3+\frac {3}{4} a^6 c^7 \left (28 b^3 c^3+120 a b^2 c^2 d+135 a^2 b c d^2+40 a^3 d^3\right ) x^4+\frac {6}{5} a^5 c^6 \left (21 b^4 c^4+140 a b^3 c^3 d+270 a^2 b^2 c^2 d^2+180 a^3 b c d^3+35 a^4 d^4\right ) x^5+3 a^4 c^5 \left (7 b^5 c^5+70 a b^4 c^4 d+210 a^2 b^3 c^3 d^2+240 a^3 b^2 c^2 d^3+105 a^4 b c d^4+14 a^5 d^5\right ) x^6+6 a^3 c^4 \left (2 b^6 c^6+30 a b^5 c^5 d+135 a^2 b^4 c^4 d^2+240 a^3 b^3 c^3 d^3+180 a^4 b^2 c^2 d^4+54 a^5 b c d^5+5 a^6 d^6\right ) x^7+\frac {3}{4} a^2 c^3 \left (6 b^7 c^7+140 a b^6 c^6 d+945 a^2 b^5 c^5 d^2+2520 a^3 b^4 c^4 d^3+2940 a^4 b^3 c^3 d^4+1512 a^5 b^2 c^2 d^5+315 a^6 b c d^6+20 a^7 d^7\right ) x^8+a c^2 \left (b^8 c^8+40 a b^7 c^7 d+420 a^2 b^6 c^6 d^2+1680 a^3 b^5 c^5 d^3+2940 a^4 b^4 c^4 d^4+2352 a^5 b^3 c^3 d^5+840 a^6 b^2 c^2 d^6+120 a^7 b c d^7+5 a^8 d^8\right ) x^9+\frac {1}{10} c \left (b^9 c^9+90 a b^8 c^8 d+1620 a^2 b^7 c^7 d^2+10080 a^3 b^6 c^6 d^3+26460 a^4 b^5 c^5 d^4+31752 a^5 b^4 c^4 d^5+17640 a^6 b^3 c^3 d^6+4320 a^7 b^2 c^2 d^7+405 a^8 b c d^8+10 a^9 d^9\right ) x^{10}+\frac {1}{11} d \left (10 b^9 c^9+405 a b^8 c^8 d+4320 a^2 b^7 c^7 d^2+17640 a^3 b^6 c^6 d^3+31752 a^4 b^5 c^5 d^4+26460 a^5 b^4 c^4 d^5+10080 a^6 b^3 c^3 d^6+1620 a^7 b^2 c^2 d^7+90 a^8 b c d^8+a^9 d^9\right ) x^{11}+\frac {3}{4} b d^2 \left (5 b^8 c^8+120 a b^7 c^7 d+840 a^2 b^6 c^6 d^2+2352 a^3 b^5 c^5 d^3+2940 a^4 b^4 c^4 d^4+1680 a^5 b^3 c^3 d^5+420 a^6 b^2 c^2 d^6+40 a^7 b c d^7+a^8 d^8\right ) x^{12}+\frac {6}{13} b^2 d^3 \left (20 b^7 c^7+315 a b^6 c^6 d+1512 a^2 b^5 c^5 d^2+2940 a^3 b^4 c^4 d^3+2520 a^4 b^3 c^3 d^4+945 a^5 b^2 c^2 d^5+140 a^6 b c d^6+6 a^7 d^7\right ) x^{13}+3 b^3 d^4 \left (5 b^6 c^6+54 a b^5 c^5 d+180 a^2 b^4 c^4 d^2+240 a^3 b^3 c^3 d^3+135 a^4 b^2 c^2 d^4+30 a^5 b c d^5+2 a^6 d^6\right ) x^{14}+\frac {6}{5} b^4 d^5 \left (14 b^5 c^5+105 a b^4 c^4 d+240 a^2 b^3 c^3 d^2+210 a^3 b^2 c^2 d^3+70 a^4 b c d^4+7 a^5 d^5\right ) x^{15}+\frac {3}{8} b^5 d^6 \left (35 b^4 c^4+180 a b^3 c^3 d+270 a^2 b^2 c^2 d^2+140 a^3 b c d^3+21 a^4 d^4\right ) x^{16}+\frac {3}{17} b^6 d^7 \left (40 b^3 c^3+135 a b^2 c^2 d+120 a^2 b c d^2+28 a^3 d^3\right ) x^{17}+\frac {1}{2} b^7 d^8 \left (5 b^2 c^2+10 a b c d+4 a^2 d^2\right ) x^{18}+\frac {1}{19} b^8 d^9 (10 b c+9 a d) x^{19}+\frac {1}{20} b^9 d^{10} x^{20} \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. \(1440\) vs.
\(2(234)=468\).
time = 0.14, size = 1441, normalized size = 5.76
method | result | size |
norman | \(\text {Expression too large to display}\) | \(1423\) |
default | \(\frac {b^{9} d^{10} x^{20}}{20}+\frac {\left (9 a \,b^{8} d^{10}+10 b^{9} c \,d^{9}\right ) x^{19}}{19}+\frac {\left (36 a^{2} b^{7} d^{10}+90 a \,b^{8} c \,d^{9}+45 b^{9} c^{2} d^{8}\right ) x^{18}}{18}+\frac {\left (84 a^{3} b^{6} d^{10}+360 a^{2} b^{7} c \,d^{9}+405 a \,b^{8} c^{2} d^{8}+120 b^{9} c^{3} d^{7}\right ) x^{17}}{17}+\frac {\left (126 a^{4} b^{5} d^{10}+840 a^{3} b^{6} c \,d^{9}+1620 a^{2} b^{7} c^{2} d^{8}+1080 a \,b^{8} c^{3} d^{7}+210 b^{9} c^{4} d^{6}\right ) x^{16}}{16}+\frac {\left (126 a^{5} b^{4} d^{10}+1260 a^{4} b^{5} c \,d^{9}+3780 a^{3} b^{6} c^{2} d^{8}+4320 a^{2} b^{7} c^{3} d^{7}+1890 a \,b^{8} c^{4} d^{6}+252 b^{9} c^{5} d^{5}\right ) x^{15}}{15}+\frac {\left (84 a^{6} b^{3} d^{10}+1260 a^{5} b^{4} c \,d^{9}+5670 a^{4} b^{5} c^{2} d^{8}+10080 a^{3} b^{6} c^{3} d^{7}+7560 a^{2} b^{7} c^{4} d^{6}+2268 a \,b^{8} c^{5} d^{5}+210 b^{9} c^{6} d^{4}\right ) x^{14}}{14}+\frac {\left (36 a^{7} b^{2} d^{10}+840 a^{6} b^{3} c \,d^{9}+5670 a^{5} b^{4} c^{2} d^{8}+15120 a^{4} b^{5} c^{3} d^{7}+17640 a^{3} b^{6} c^{4} d^{6}+9072 a^{2} b^{7} c^{5} d^{5}+1890 a \,b^{8} c^{6} d^{4}+120 b^{9} c^{7} d^{3}\right ) x^{13}}{13}+\frac {\left (9 a^{8} b \,d^{10}+360 a^{7} b^{2} c \,d^{9}+3780 a^{6} b^{3} c^{2} d^{8}+15120 a^{5} b^{4} c^{3} d^{7}+26460 a^{4} b^{5} c^{4} d^{6}+21168 a^{3} b^{6} c^{5} d^{5}+7560 a^{2} b^{7} c^{6} d^{4}+1080 a \,b^{8} c^{7} d^{3}+45 b^{9} c^{8} d^{2}\right ) x^{12}}{12}+\frac {\left (a^{9} d^{10}+90 a^{8} b c \,d^{9}+1620 a^{7} b^{2} c^{2} d^{8}+10080 a^{6} b^{3} c^{3} d^{7}+26460 a^{5} b^{4} c^{4} d^{6}+31752 a^{4} b^{5} c^{5} d^{5}+17640 a^{3} b^{6} c^{6} d^{4}+4320 a^{2} b^{7} c^{7} d^{3}+405 a \,b^{8} c^{8} d^{2}+10 b^{9} c^{9} d \right ) x^{11}}{11}+\frac {\left (10 a^{9} c \,d^{9}+405 a^{8} b \,c^{2} d^{8}+4320 a^{7} b^{2} c^{3} d^{7}+17640 a^{6} b^{3} c^{4} d^{6}+31752 a^{5} b^{4} c^{5} d^{5}+26460 a^{4} b^{5} c^{6} d^{4}+10080 a^{3} b^{6} c^{7} d^{3}+1620 a^{2} b^{7} c^{8} d^{2}+90 a \,b^{8} c^{9} d +b^{9} c^{10}\right ) x^{10}}{10}+\frac {\left (45 a^{9} c^{2} d^{8}+1080 a^{8} b \,c^{3} d^{7}+7560 a^{7} b^{2} c^{4} d^{6}+21168 a^{6} b^{3} c^{5} d^{5}+26460 a^{5} b^{4} c^{6} d^{4}+15120 a^{4} b^{5} c^{7} d^{3}+3780 a^{3} b^{6} c^{8} d^{2}+360 a^{2} b^{7} c^{9} d +9 a \,b^{8} c^{10}\right ) x^{9}}{9}+\frac {\left (120 a^{9} c^{3} d^{7}+1890 a^{8} b \,c^{4} d^{6}+9072 a^{7} b^{2} c^{5} d^{5}+17640 a^{6} b^{3} c^{6} d^{4}+15120 a^{5} b^{4} c^{7} d^{3}+5670 a^{4} b^{5} c^{8} d^{2}+840 a^{3} b^{6} c^{9} d +36 a^{2} b^{7} c^{10}\right ) x^{8}}{8}+\frac {\left (210 a^{9} c^{4} d^{6}+2268 a^{8} b \,c^{5} d^{5}+7560 a^{7} b^{2} c^{6} d^{4}+10080 a^{6} b^{3} c^{7} d^{3}+5670 a^{5} b^{4} c^{8} d^{2}+1260 a^{4} b^{5} c^{9} d +84 a^{3} b^{6} c^{10}\right ) x^{7}}{7}+\frac {\left (252 a^{9} c^{5} d^{5}+1890 a^{8} b \,c^{6} d^{4}+4320 a^{7} b^{2} c^{7} d^{3}+3780 a^{6} b^{3} c^{8} d^{2}+1260 a^{5} b^{4} c^{9} d +126 a^{4} b^{5} c^{10}\right ) x^{6}}{6}+\frac {\left (210 a^{9} c^{6} d^{4}+1080 a^{8} b \,c^{7} d^{3}+1620 a^{7} b^{2} c^{8} d^{2}+840 a^{6} b^{3} c^{9} d +126 a^{5} b^{4} c^{10}\right ) x^{5}}{5}+\frac {\left (120 a^{9} c^{7} d^{3}+405 a^{8} b \,c^{8} d^{2}+360 a^{7} b^{2} c^{9} d +84 a^{6} b^{3} c^{10}\right ) x^{4}}{4}+\frac {\left (45 a^{9} c^{8} d^{2}+90 a^{8} b \,c^{9} d +36 a^{7} b^{2} c^{10}\right ) x^{3}}{3}+\frac {\left (10 a^{9} c^{9} d +9 a^{8} b \,c^{10}\right ) x^{2}}{2}+a^{9} c^{10} x\) | \(1441\) |
gosper | \(\text {Expression too large to display}\) | \(1657\) |
risch | \(\text {Expression too large to display}\) | \(1657\) |
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. 1437 vs.
\(2 (234) = 468\).
time = 0.29, size = 1437, normalized size = 5.75 \begin {gather*} \frac {1}{20} \, b^{9} d^{10} x^{20} + a^{9} c^{10} x + \frac {1}{19} \, {\left (10 \, b^{9} c d^{9} + 9 \, a b^{8} d^{10}\right )} x^{19} + \frac {1}{2} \, {\left (5 \, b^{9} c^{2} d^{8} + 10 \, a b^{8} c d^{9} + 4 \, a^{2} b^{7} d^{10}\right )} x^{18} + \frac {3}{17} \, {\left (40 \, b^{9} c^{3} d^{7} + 135 \, a b^{8} c^{2} d^{8} + 120 \, a^{2} b^{7} c d^{9} + 28 \, a^{3} b^{6} d^{10}\right )} x^{17} + \frac {3}{8} \, {\left (35 \, b^{9} c^{4} d^{6} + 180 \, a b^{8} c^{3} d^{7} + 270 \, a^{2} b^{7} c^{2} d^{8} + 140 \, a^{3} b^{6} c d^{9} + 21 \, a^{4} b^{5} d^{10}\right )} x^{16} + \frac {6}{5} \, {\left (14 \, b^{9} c^{5} d^{5} + 105 \, a b^{8} c^{4} d^{6} + 240 \, a^{2} b^{7} c^{3} d^{7} + 210 \, a^{3} b^{6} c^{2} d^{8} + 70 \, a^{4} b^{5} c d^{9} + 7 \, a^{5} b^{4} d^{10}\right )} x^{15} + 3 \, {\left (5 \, b^{9} c^{6} d^{4} + 54 \, a b^{8} c^{5} d^{5} + 180 \, a^{2} b^{7} c^{4} d^{6} + 240 \, a^{3} b^{6} c^{3} d^{7} + 135 \, a^{4} b^{5} c^{2} d^{8} + 30 \, a^{5} b^{4} c d^{9} + 2 \, a^{6} b^{3} d^{10}\right )} x^{14} + \frac {6}{13} \, {\left (20 \, b^{9} c^{7} d^{3} + 315 \, a b^{8} c^{6} d^{4} + 1512 \, a^{2} b^{7} c^{5} d^{5} + 2940 \, a^{3} b^{6} c^{4} d^{6} + 2520 \, a^{4} b^{5} c^{3} d^{7} + 945 \, a^{5} b^{4} c^{2} d^{8} + 140 \, a^{6} b^{3} c d^{9} + 6 \, a^{7} b^{2} d^{10}\right )} x^{13} + \frac {3}{4} \, {\left (5 \, b^{9} c^{8} d^{2} + 120 \, a b^{8} c^{7} d^{3} + 840 \, a^{2} b^{7} c^{6} d^{4} + 2352 \, a^{3} b^{6} c^{5} d^{5} + 2940 \, a^{4} b^{5} c^{4} d^{6} + 1680 \, a^{5} b^{4} c^{3} d^{7} + 420 \, a^{6} b^{3} c^{2} d^{8} + 40 \, a^{7} b^{2} c d^{9} + a^{8} b d^{10}\right )} x^{12} + \frac {1}{11} \, {\left (10 \, b^{9} c^{9} d + 405 \, a b^{8} c^{8} d^{2} + 4320 \, a^{2} b^{7} c^{7} d^{3} + 17640 \, a^{3} b^{6} c^{6} d^{4} + 31752 \, a^{4} b^{5} c^{5} d^{5} + 26460 \, a^{5} b^{4} c^{4} d^{6} + 10080 \, a^{6} b^{3} c^{3} d^{7} + 1620 \, a^{7} b^{2} c^{2} d^{8} + 90 \, a^{8} b c d^{9} + a^{9} d^{10}\right )} x^{11} + \frac {1}{10} \, {\left (b^{9} c^{10} + 90 \, a b^{8} c^{9} d + 1620 \, a^{2} b^{7} c^{8} d^{2} + 10080 \, a^{3} b^{6} c^{7} d^{3} + 26460 \, a^{4} b^{5} c^{6} d^{4} + 31752 \, a^{5} b^{4} c^{5} d^{5} + 17640 \, a^{6} b^{3} c^{4} d^{6} + 4320 \, a^{7} b^{2} c^{3} d^{7} + 405 \, a^{8} b c^{2} d^{8} + 10 \, a^{9} c d^{9}\right )} x^{10} + {\left (a b^{8} c^{10} + 40 \, a^{2} b^{7} c^{9} d + 420 \, a^{3} b^{6} c^{8} d^{2} + 1680 \, a^{4} b^{5} c^{7} d^{3} + 2940 \, a^{5} b^{4} c^{6} d^{4} + 2352 \, a^{6} b^{3} c^{5} d^{5} + 840 \, a^{7} b^{2} c^{4} d^{6} + 120 \, a^{8} b c^{3} d^{7} + 5 \, a^{9} c^{2} d^{8}\right )} x^{9} + \frac {3}{4} \, {\left (6 \, a^{2} b^{7} c^{10} + 140 \, a^{3} b^{6} c^{9} d + 945 \, a^{4} b^{5} c^{8} d^{2} + 2520 \, a^{5} b^{4} c^{7} d^{3} + 2940 \, a^{6} b^{3} c^{6} d^{4} + 1512 \, a^{7} b^{2} c^{5} d^{5} + 315 \, a^{8} b c^{4} d^{6} + 20 \, a^{9} c^{3} d^{7}\right )} x^{8} + 6 \, {\left (2 \, a^{3} b^{6} c^{10} + 30 \, a^{4} b^{5} c^{9} d + 135 \, a^{5} b^{4} c^{8} d^{2} + 240 \, a^{6} b^{3} c^{7} d^{3} + 180 \, a^{7} b^{2} c^{6} d^{4} + 54 \, a^{8} b c^{5} d^{5} + 5 \, a^{9} c^{4} d^{6}\right )} x^{7} + 3 \, {\left (7 \, a^{4} b^{5} c^{10} + 70 \, a^{5} b^{4} c^{9} d + 210 \, a^{6} b^{3} c^{8} d^{2} + 240 \, a^{7} b^{2} c^{7} d^{3} + 105 \, a^{8} b c^{6} d^{4} + 14 \, a^{9} c^{5} d^{5}\right )} x^{6} + \frac {6}{5} \, {\left (21 \, a^{5} b^{4} c^{10} + 140 \, a^{6} b^{3} c^{9} d + 270 \, a^{7} b^{2} c^{8} d^{2} + 180 \, a^{8} b c^{7} d^{3} + 35 \, a^{9} c^{6} d^{4}\right )} x^{5} + \frac {3}{4} \, {\left (28 \, a^{6} b^{3} c^{10} + 120 \, a^{7} b^{2} c^{9} d + 135 \, a^{8} b c^{8} d^{2} + 40 \, a^{9} c^{7} d^{3}\right )} x^{4} + 3 \, {\left (4 \, a^{7} b^{2} c^{10} + 10 \, a^{8} b c^{9} d + 5 \, a^{9} c^{8} d^{2}\right )} x^{3} + \frac {1}{2} \, {\left (9 \, a^{8} b c^{10} + 10 \, a^{9} c^{9} d\right )} x^{2} \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. 1437 vs.
\(2 (234) = 468\).
time = 0.55, size = 1437, normalized size = 5.75 \begin {gather*} \frac {1}{20} \, b^{9} d^{10} x^{20} + a^{9} c^{10} x + \frac {1}{19} \, {\left (10 \, b^{9} c d^{9} + 9 \, a b^{8} d^{10}\right )} x^{19} + \frac {1}{2} \, {\left (5 \, b^{9} c^{2} d^{8} + 10 \, a b^{8} c d^{9} + 4 \, a^{2} b^{7} d^{10}\right )} x^{18} + \frac {3}{17} \, {\left (40 \, b^{9} c^{3} d^{7} + 135 \, a b^{8} c^{2} d^{8} + 120 \, a^{2} b^{7} c d^{9} + 28 \, a^{3} b^{6} d^{10}\right )} x^{17} + \frac {3}{8} \, {\left (35 \, b^{9} c^{4} d^{6} + 180 \, a b^{8} c^{3} d^{7} + 270 \, a^{2} b^{7} c^{2} d^{8} + 140 \, a^{3} b^{6} c d^{9} + 21 \, a^{4} b^{5} d^{10}\right )} x^{16} + \frac {6}{5} \, {\left (14 \, b^{9} c^{5} d^{5} + 105 \, a b^{8} c^{4} d^{6} + 240 \, a^{2} b^{7} c^{3} d^{7} + 210 \, a^{3} b^{6} c^{2} d^{8} + 70 \, a^{4} b^{5} c d^{9} + 7 \, a^{5} b^{4} d^{10}\right )} x^{15} + 3 \, {\left (5 \, b^{9} c^{6} d^{4} + 54 \, a b^{8} c^{5} d^{5} + 180 \, a^{2} b^{7} c^{4} d^{6} + 240 \, a^{3} b^{6} c^{3} d^{7} + 135 \, a^{4} b^{5} c^{2} d^{8} + 30 \, a^{5} b^{4} c d^{9} + 2 \, a^{6} b^{3} d^{10}\right )} x^{14} + \frac {6}{13} \, {\left (20 \, b^{9} c^{7} d^{3} + 315 \, a b^{8} c^{6} d^{4} + 1512 \, a^{2} b^{7} c^{5} d^{5} + 2940 \, a^{3} b^{6} c^{4} d^{6} + 2520 \, a^{4} b^{5} c^{3} d^{7} + 945 \, a^{5} b^{4} c^{2} d^{8} + 140 \, a^{6} b^{3} c d^{9} + 6 \, a^{7} b^{2} d^{10}\right )} x^{13} + \frac {3}{4} \, {\left (5 \, b^{9} c^{8} d^{2} + 120 \, a b^{8} c^{7} d^{3} + 840 \, a^{2} b^{7} c^{6} d^{4} + 2352 \, a^{3} b^{6} c^{5} d^{5} + 2940 \, a^{4} b^{5} c^{4} d^{6} + 1680 \, a^{5} b^{4} c^{3} d^{7} + 420 \, a^{6} b^{3} c^{2} d^{8} + 40 \, a^{7} b^{2} c d^{9} + a^{8} b d^{10}\right )} x^{12} + \frac {1}{11} \, {\left (10 \, b^{9} c^{9} d + 405 \, a b^{8} c^{8} d^{2} + 4320 \, a^{2} b^{7} c^{7} d^{3} + 17640 \, a^{3} b^{6} c^{6} d^{4} + 31752 \, a^{4} b^{5} c^{5} d^{5} + 26460 \, a^{5} b^{4} c^{4} d^{6} + 10080 \, a^{6} b^{3} c^{3} d^{7} + 1620 \, a^{7} b^{2} c^{2} d^{8} + 90 \, a^{8} b c d^{9} + a^{9} d^{10}\right )} x^{11} + \frac {1}{10} \, {\left (b^{9} c^{10} + 90 \, a b^{8} c^{9} d + 1620 \, a^{2} b^{7} c^{8} d^{2} + 10080 \, a^{3} b^{6} c^{7} d^{3} + 26460 \, a^{4} b^{5} c^{6} d^{4} + 31752 \, a^{5} b^{4} c^{5} d^{5} + 17640 \, a^{6} b^{3} c^{4} d^{6} + 4320 \, a^{7} b^{2} c^{3} d^{7} + 405 \, a^{8} b c^{2} d^{8} + 10 \, a^{9} c d^{9}\right )} x^{10} + {\left (a b^{8} c^{10} + 40 \, a^{2} b^{7} c^{9} d + 420 \, a^{3} b^{6} c^{8} d^{2} + 1680 \, a^{4} b^{5} c^{7} d^{3} + 2940 \, a^{5} b^{4} c^{6} d^{4} + 2352 \, a^{6} b^{3} c^{5} d^{5} + 840 \, a^{7} b^{2} c^{4} d^{6} + 120 \, a^{8} b c^{3} d^{7} + 5 \, a^{9} c^{2} d^{8}\right )} x^{9} + \frac {3}{4} \, {\left (6 \, a^{2} b^{7} c^{10} + 140 \, a^{3} b^{6} c^{9} d + 945 \, a^{4} b^{5} c^{8} d^{2} + 2520 \, a^{5} b^{4} c^{7} d^{3} + 2940 \, a^{6} b^{3} c^{6} d^{4} + 1512 \, a^{7} b^{2} c^{5} d^{5} + 315 \, a^{8} b c^{4} d^{6} + 20 \, a^{9} c^{3} d^{7}\right )} x^{8} + 6 \, {\left (2 \, a^{3} b^{6} c^{10} + 30 \, a^{4} b^{5} c^{9} d + 135 \, a^{5} b^{4} c^{8} d^{2} + 240 \, a^{6} b^{3} c^{7} d^{3} + 180 \, a^{7} b^{2} c^{6} d^{4} + 54 \, a^{8} b c^{5} d^{5} + 5 \, a^{9} c^{4} d^{6}\right )} x^{7} + 3 \, {\left (7 \, a^{4} b^{5} c^{10} + 70 \, a^{5} b^{4} c^{9} d + 210 \, a^{6} b^{3} c^{8} d^{2} + 240 \, a^{7} b^{2} c^{7} d^{3} + 105 \, a^{8} b c^{6} d^{4} + 14 \, a^{9} c^{5} d^{5}\right )} x^{6} + \frac {6}{5} \, {\left (21 \, a^{5} b^{4} c^{10} + 140 \, a^{6} b^{3} c^{9} d + 270 \, a^{7} b^{2} c^{8} d^{2} + 180 \, a^{8} b c^{7} d^{3} + 35 \, a^{9} c^{6} d^{4}\right )} x^{5} + \frac {3}{4} \, {\left (28 \, a^{6} b^{3} c^{10} + 120 \, a^{7} b^{2} c^{9} d + 135 \, a^{8} b c^{8} d^{2} + 40 \, a^{9} c^{7} d^{3}\right )} x^{4} + 3 \, {\left (4 \, a^{7} b^{2} c^{10} + 10 \, a^{8} b c^{9} d + 5 \, a^{9} c^{8} d^{2}\right )} x^{3} + \frac {1}{2} \, {\left (9 \, a^{8} b c^{10} + 10 \, a^{9} c^{9} d\right )} x^{2} \end {gather*}
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. 1598 vs.
\(2 (231) = 462\).
time = 0.11, size = 1598, normalized size = 6.39 \begin {gather*} a^{9} c^{10} x + \frac {b^{9} d^{10} x^{20}}{20} + x^{19} \cdot \left (\frac {9 a b^{8} d^{10}}{19} + \frac {10 b^{9} c d^{9}}{19}\right ) + x^{18} \cdot \left (2 a^{2} b^{7} d^{10} + 5 a b^{8} c d^{9} + \frac {5 b^{9} c^{2} d^{8}}{2}\right ) + x^{17} \cdot \left (\frac {84 a^{3} b^{6} d^{10}}{17} + \frac {360 a^{2} b^{7} c d^{9}}{17} + \frac {405 a b^{8} c^{2} d^{8}}{17} + \frac {120 b^{9} c^{3} d^{7}}{17}\right ) + x^{16} \cdot \left (\frac {63 a^{4} b^{5} d^{10}}{8} + \frac {105 a^{3} b^{6} c d^{9}}{2} + \frac {405 a^{2} b^{7} c^{2} d^{8}}{4} + \frac {135 a b^{8} c^{3} d^{7}}{2} + \frac {105 b^{9} c^{4} d^{6}}{8}\right ) + x^{15} \cdot \left (\frac {42 a^{5} b^{4} d^{10}}{5} + 84 a^{4} b^{5} c d^{9} + 252 a^{3} b^{6} c^{2} d^{8} + 288 a^{2} b^{7} c^{3} d^{7} + 126 a b^{8} c^{4} d^{6} + \frac {84 b^{9} c^{5} d^{5}}{5}\right ) + x^{14} \cdot \left (6 a^{6} b^{3} d^{10} + 90 a^{5} b^{4} c d^{9} + 405 a^{4} b^{5} c^{2} d^{8} + 720 a^{3} b^{6} c^{3} d^{7} + 540 a^{2} b^{7} c^{4} d^{6} + 162 a b^{8} c^{5} d^{5} + 15 b^{9} c^{6} d^{4}\right ) + x^{13} \cdot \left (\frac {36 a^{7} b^{2} d^{10}}{13} + \frac {840 a^{6} b^{3} c d^{9}}{13} + \frac {5670 a^{5} b^{4} c^{2} d^{8}}{13} + \frac {15120 a^{4} b^{5} c^{3} d^{7}}{13} + \frac {17640 a^{3} b^{6} c^{4} d^{6}}{13} + \frac {9072 a^{2} b^{7} c^{5} d^{5}}{13} + \frac {1890 a b^{8} c^{6} d^{4}}{13} + \frac {120 b^{9} c^{7} d^{3}}{13}\right ) + x^{12} \cdot \left (\frac {3 a^{8} b d^{10}}{4} + 30 a^{7} b^{2} c d^{9} + 315 a^{6} b^{3} c^{2} d^{8} + 1260 a^{5} b^{4} c^{3} d^{7} + 2205 a^{4} b^{5} c^{4} d^{6} + 1764 a^{3} b^{6} c^{5} d^{5} + 630 a^{2} b^{7} c^{6} d^{4} + 90 a b^{8} c^{7} d^{3} + \frac {15 b^{9} c^{8} d^{2}}{4}\right ) + x^{11} \left (\frac {a^{9} d^{10}}{11} + \frac {90 a^{8} b c d^{9}}{11} + \frac {1620 a^{7} b^{2} c^{2} d^{8}}{11} + \frac {10080 a^{6} b^{3} c^{3} d^{7}}{11} + \frac {26460 a^{5} b^{4} c^{4} d^{6}}{11} + \frac {31752 a^{4} b^{5} c^{5} d^{5}}{11} + \frac {17640 a^{3} b^{6} c^{6} d^{4}}{11} + \frac {4320 a^{2} b^{7} c^{7} d^{3}}{11} + \frac {405 a b^{8} c^{8} d^{2}}{11} + \frac {10 b^{9} c^{9} d}{11}\right ) + x^{10} \left (a^{9} c d^{9} + \frac {81 a^{8} b c^{2} d^{8}}{2} + 432 a^{7} b^{2} c^{3} d^{7} + 1764 a^{6} b^{3} c^{4} d^{6} + \frac {15876 a^{5} b^{4} c^{5} d^{5}}{5} + 2646 a^{4} b^{5} c^{6} d^{4} + 1008 a^{3} b^{6} c^{7} d^{3} + 162 a^{2} b^{7} c^{8} d^{2} + 9 a b^{8} c^{9} d + \frac {b^{9} c^{10}}{10}\right ) + x^{9} \cdot \left (5 a^{9} c^{2} d^{8} + 120 a^{8} b c^{3} d^{7} + 840 a^{7} b^{2} c^{4} d^{6} + 2352 a^{6} b^{3} c^{5} d^{5} + 2940 a^{5} b^{4} c^{6} d^{4} + 1680 a^{4} b^{5} c^{7} d^{3} + 420 a^{3} b^{6} c^{8} d^{2} + 40 a^{2} b^{7} c^{9} d + a b^{8} c^{10}\right ) + x^{8} \cdot \left (15 a^{9} c^{3} d^{7} + \frac {945 a^{8} b c^{4} d^{6}}{4} + 1134 a^{7} b^{2} c^{5} d^{5} + 2205 a^{6} b^{3} c^{6} d^{4} + 1890 a^{5} b^{4} c^{7} d^{3} + \frac {2835 a^{4} b^{5} c^{8} d^{2}}{4} + 105 a^{3} b^{6} c^{9} d + \frac {9 a^{2} b^{7} c^{10}}{2}\right ) + x^{7} \cdot \left (30 a^{9} c^{4} d^{6} + 324 a^{8} b c^{5} d^{5} + 1080 a^{7} b^{2} c^{6} d^{4} + 1440 a^{6} b^{3} c^{7} d^{3} + 810 a^{5} b^{4} c^{8} d^{2} + 180 a^{4} b^{5} c^{9} d + 12 a^{3} b^{6} c^{10}\right ) + x^{6} \cdot \left (42 a^{9} c^{5} d^{5} + 315 a^{8} b c^{6} d^{4} + 720 a^{7} b^{2} c^{7} d^{3} + 630 a^{6} b^{3} c^{8} d^{2} + 210 a^{5} b^{4} c^{9} d + 21 a^{4} b^{5} c^{10}\right ) + x^{5} \cdot \left (42 a^{9} c^{6} d^{4} + 216 a^{8} b c^{7} d^{3} + 324 a^{7} b^{2} c^{8} d^{2} + 168 a^{6} b^{3} c^{9} d + \frac {126 a^{5} b^{4} c^{10}}{5}\right ) + x^{4} \cdot \left (30 a^{9} c^{7} d^{3} + \frac {405 a^{8} b c^{8} d^{2}}{4} + 90 a^{7} b^{2} c^{9} d + 21 a^{6} b^{3} c^{10}\right ) + x^{3} \cdot \left (15 a^{9} c^{8} d^{2} + 30 a^{8} b c^{9} d + 12 a^{7} b^{2} c^{10}\right ) + x^{2} \cdot \left (5 a^{9} c^{9} d + \frac {9 a^{8} b c^{10}}{2}\right ) \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. 1656 vs.
\(2 (234) = 468\).
time = 0.90, size = 1656, normalized size = 6.62 \begin {gather*} \frac {1}{20} \, b^{9} d^{10} x^{20} + \frac {10}{19} \, b^{9} c d^{9} x^{19} + \frac {9}{19} \, a b^{8} d^{10} x^{19} + \frac {5}{2} \, b^{9} c^{2} d^{8} x^{18} + 5 \, a b^{8} c d^{9} x^{18} + 2 \, a^{2} b^{7} d^{10} x^{18} + \frac {120}{17} \, b^{9} c^{3} d^{7} x^{17} + \frac {405}{17} \, a b^{8} c^{2} d^{8} x^{17} + \frac {360}{17} \, a^{2} b^{7} c d^{9} x^{17} + \frac {84}{17} \, a^{3} b^{6} d^{10} x^{17} + \frac {105}{8} \, b^{9} c^{4} d^{6} x^{16} + \frac {135}{2} \, a b^{8} c^{3} d^{7} x^{16} + \frac {405}{4} \, a^{2} b^{7} c^{2} d^{8} x^{16} + \frac {105}{2} \, a^{3} b^{6} c d^{9} x^{16} + \frac {63}{8} \, a^{4} b^{5} d^{10} x^{16} + \frac {84}{5} \, b^{9} c^{5} d^{5} x^{15} + 126 \, a b^{8} c^{4} d^{6} x^{15} + 288 \, a^{2} b^{7} c^{3} d^{7} x^{15} + 252 \, a^{3} b^{6} c^{2} d^{8} x^{15} + 84 \, a^{4} b^{5} c d^{9} x^{15} + \frac {42}{5} \, a^{5} b^{4} d^{10} x^{15} + 15 \, b^{9} c^{6} d^{4} x^{14} + 162 \, a b^{8} c^{5} d^{5} x^{14} + 540 \, a^{2} b^{7} c^{4} d^{6} x^{14} + 720 \, a^{3} b^{6} c^{3} d^{7} x^{14} + 405 \, a^{4} b^{5} c^{2} d^{8} x^{14} + 90 \, a^{5} b^{4} c d^{9} x^{14} + 6 \, a^{6} b^{3} d^{10} x^{14} + \frac {120}{13} \, b^{9} c^{7} d^{3} x^{13} + \frac {1890}{13} \, a b^{8} c^{6} d^{4} x^{13} + \frac {9072}{13} \, a^{2} b^{7} c^{5} d^{5} x^{13} + \frac {17640}{13} \, a^{3} b^{6} c^{4} d^{6} x^{13} + \frac {15120}{13} \, a^{4} b^{5} c^{3} d^{7} x^{13} + \frac {5670}{13} \, a^{5} b^{4} c^{2} d^{8} x^{13} + \frac {840}{13} \, a^{6} b^{3} c d^{9} x^{13} + \frac {36}{13} \, a^{7} b^{2} d^{10} x^{13} + \frac {15}{4} \, b^{9} c^{8} d^{2} x^{12} + 90 \, a b^{8} c^{7} d^{3} x^{12} + 630 \, a^{2} b^{7} c^{6} d^{4} x^{12} + 1764 \, a^{3} b^{6} c^{5} d^{5} x^{12} + 2205 \, a^{4} b^{5} c^{4} d^{6} x^{12} + 1260 \, a^{5} b^{4} c^{3} d^{7} x^{12} + 315 \, a^{6} b^{3} c^{2} d^{8} x^{12} + 30 \, a^{7} b^{2} c d^{9} x^{12} + \frac {3}{4} \, a^{8} b d^{10} x^{12} + \frac {10}{11} \, b^{9} c^{9} d x^{11} + \frac {405}{11} \, a b^{8} c^{8} d^{2} x^{11} + \frac {4320}{11} \, a^{2} b^{7} c^{7} d^{3} x^{11} + \frac {17640}{11} \, a^{3} b^{6} c^{6} d^{4} x^{11} + \frac {31752}{11} \, a^{4} b^{5} c^{5} d^{5} x^{11} + \frac {26460}{11} \, a^{5} b^{4} c^{4} d^{6} x^{11} + \frac {10080}{11} \, a^{6} b^{3} c^{3} d^{7} x^{11} + \frac {1620}{11} \, a^{7} b^{2} c^{2} d^{8} x^{11} + \frac {90}{11} \, a^{8} b c d^{9} x^{11} + \frac {1}{11} \, a^{9} d^{10} x^{11} + \frac {1}{10} \, b^{9} c^{10} x^{10} + 9 \, a b^{8} c^{9} d x^{10} + 162 \, a^{2} b^{7} c^{8} d^{2} x^{10} + 1008 \, a^{3} b^{6} c^{7} d^{3} x^{10} + 2646 \, a^{4} b^{5} c^{6} d^{4} x^{10} + \frac {15876}{5} \, a^{5} b^{4} c^{5} d^{5} x^{10} + 1764 \, a^{6} b^{3} c^{4} d^{6} x^{10} + 432 \, a^{7} b^{2} c^{3} d^{7} x^{10} + \frac {81}{2} \, a^{8} b c^{2} d^{8} x^{10} + a^{9} c d^{9} x^{10} + a b^{8} c^{10} x^{9} + 40 \, a^{2} b^{7} c^{9} d x^{9} + 420 \, a^{3} b^{6} c^{8} d^{2} x^{9} + 1680 \, a^{4} b^{5} c^{7} d^{3} x^{9} + 2940 \, a^{5} b^{4} c^{6} d^{4} x^{9} + 2352 \, a^{6} b^{3} c^{5} d^{5} x^{9} + 840 \, a^{7} b^{2} c^{4} d^{6} x^{9} + 120 \, a^{8} b c^{3} d^{7} x^{9} + 5 \, a^{9} c^{2} d^{8} x^{9} + \frac {9}{2} \, a^{2} b^{7} c^{10} x^{8} + 105 \, a^{3} b^{6} c^{9} d x^{8} + \frac {2835}{4} \, a^{4} b^{5} c^{8} d^{2} x^{8} + 1890 \, a^{5} b^{4} c^{7} d^{3} x^{8} + 2205 \, a^{6} b^{3} c^{6} d^{4} x^{8} + 1134 \, a^{7} b^{2} c^{5} d^{5} x^{8} + \frac {945}{4} \, a^{8} b c^{4} d^{6} x^{8} + 15 \, a^{9} c^{3} d^{7} x^{8} + 12 \, a^{3} b^{6} c^{10} x^{7} + 180 \, a^{4} b^{5} c^{9} d x^{7} + 810 \, a^{5} b^{4} c^{8} d^{2} x^{7} + 1440 \, a^{6} b^{3} c^{7} d^{3} x^{7} + 1080 \, a^{7} b^{2} c^{6} d^{4} x^{7} + 324 \, a^{8} b c^{5} d^{5} x^{7} + 30 \, a^{9} c^{4} d^{6} x^{7} + 21 \, a^{4} b^{5} c^{10} x^{6} + 210 \, a^{5} b^{4} c^{9} d x^{6} + 630 \, a^{6} b^{3} c^{8} d^{2} x^{6} + 720 \, a^{7} b^{2} c^{7} d^{3} x^{6} + 315 \, a^{8} b c^{6} d^{4} x^{6} + 42 \, a^{9} c^{5} d^{5} x^{6} + \frac {126}{5} \, a^{5} b^{4} c^{10} x^{5} + 168 \, a^{6} b^{3} c^{9} d x^{5} + 324 \, a^{7} b^{2} c^{8} d^{2} x^{5} + 216 \, a^{8} b c^{7} d^{3} x^{5} + 42 \, a^{9} c^{6} d^{4} x^{5} + 21 \, a^{6} b^{3} c^{10} x^{4} + 90 \, a^{7} b^{2} c^{9} d x^{4} + \frac {405}{4} \, a^{8} b c^{8} d^{2} x^{4} + 30 \, a^{9} c^{7} d^{3} x^{4} + 12 \, a^{7} b^{2} c^{10} x^{3} + 30 \, a^{8} b c^{9} d x^{3} + 15 \, a^{9} c^{8} d^{2} x^{3} + \frac {9}{2} \, a^{8} b c^{10} x^{2} + 5 \, a^{9} c^{9} d x^{2} + a^{9} c^{10} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.79, size = 1404, normalized size = 5.62 \begin {gather*} x^7\,\left (30\,a^9\,c^4\,d^6+324\,a^8\,b\,c^5\,d^5+1080\,a^7\,b^2\,c^6\,d^4+1440\,a^6\,b^3\,c^7\,d^3+810\,a^5\,b^4\,c^8\,d^2+180\,a^4\,b^5\,c^9\,d+12\,a^3\,b^6\,c^{10}\right )+x^{14}\,\left (6\,a^6\,b^3\,d^{10}+90\,a^5\,b^4\,c\,d^9+405\,a^4\,b^5\,c^2\,d^8+720\,a^3\,b^6\,c^3\,d^7+540\,a^2\,b^7\,c^4\,d^6+162\,a\,b^8\,c^5\,d^5+15\,b^9\,c^6\,d^4\right )+x^5\,\left (42\,a^9\,c^6\,d^4+216\,a^8\,b\,c^7\,d^3+324\,a^7\,b^2\,c^8\,d^2+168\,a^6\,b^3\,c^9\,d+\frac {126\,a^5\,b^4\,c^{10}}{5}\right )+x^{16}\,\left (\frac {63\,a^4\,b^5\,d^{10}}{8}+\frac {105\,a^3\,b^6\,c\,d^9}{2}+\frac {405\,a^2\,b^7\,c^2\,d^8}{4}+\frac {135\,a\,b^8\,c^3\,d^7}{2}+\frac {105\,b^9\,c^4\,d^6}{8}\right )+x^8\,\left (15\,a^9\,c^3\,d^7+\frac {945\,a^8\,b\,c^4\,d^6}{4}+1134\,a^7\,b^2\,c^5\,d^5+2205\,a^6\,b^3\,c^6\,d^4+1890\,a^5\,b^4\,c^7\,d^3+\frac {2835\,a^4\,b^5\,c^8\,d^2}{4}+105\,a^3\,b^6\,c^9\,d+\frac {9\,a^2\,b^7\,c^{10}}{2}\right )+x^{13}\,\left (\frac {36\,a^7\,b^2\,d^{10}}{13}+\frac {840\,a^6\,b^3\,c\,d^9}{13}+\frac {5670\,a^5\,b^4\,c^2\,d^8}{13}+\frac {15120\,a^4\,b^5\,c^3\,d^7}{13}+\frac {17640\,a^3\,b^6\,c^4\,d^6}{13}+\frac {9072\,a^2\,b^7\,c^5\,d^5}{13}+\frac {1890\,a\,b^8\,c^6\,d^4}{13}+\frac {120\,b^9\,c^7\,d^3}{13}\right )+x^9\,\left (5\,a^9\,c^2\,d^8+120\,a^8\,b\,c^3\,d^7+840\,a^7\,b^2\,c^4\,d^6+2352\,a^6\,b^3\,c^5\,d^5+2940\,a^5\,b^4\,c^6\,d^4+1680\,a^4\,b^5\,c^7\,d^3+420\,a^3\,b^6\,c^8\,d^2+40\,a^2\,b^7\,c^9\,d+a\,b^8\,c^{10}\right )+x^{12}\,\left (\frac {3\,a^8\,b\,d^{10}}{4}+30\,a^7\,b^2\,c\,d^9+315\,a^6\,b^3\,c^2\,d^8+1260\,a^5\,b^4\,c^3\,d^7+2205\,a^4\,b^5\,c^4\,d^6+1764\,a^3\,b^6\,c^5\,d^5+630\,a^2\,b^7\,c^6\,d^4+90\,a\,b^8\,c^7\,d^3+\frac {15\,b^9\,c^8\,d^2}{4}\right )+x^6\,\left (42\,a^9\,c^5\,d^5+315\,a^8\,b\,c^6\,d^4+720\,a^7\,b^2\,c^7\,d^3+630\,a^6\,b^3\,c^8\,d^2+210\,a^5\,b^4\,c^9\,d+21\,a^4\,b^5\,c^{10}\right )+x^{15}\,\left (\frac {42\,a^5\,b^4\,d^{10}}{5}+84\,a^4\,b^5\,c\,d^9+252\,a^3\,b^6\,c^2\,d^8+288\,a^2\,b^7\,c^3\,d^7+126\,a\,b^8\,c^4\,d^6+\frac {84\,b^9\,c^5\,d^5}{5}\right )+x^{10}\,\left (a^9\,c\,d^9+\frac {81\,a^8\,b\,c^2\,d^8}{2}+432\,a^7\,b^2\,c^3\,d^7+1764\,a^6\,b^3\,c^4\,d^6+\frac {15876\,a^5\,b^4\,c^5\,d^5}{5}+2646\,a^4\,b^5\,c^6\,d^4+1008\,a^3\,b^6\,c^7\,d^3+162\,a^2\,b^7\,c^8\,d^2+9\,a\,b^8\,c^9\,d+\frac {b^9\,c^{10}}{10}\right )+x^{11}\,\left (\frac {a^9\,d^{10}}{11}+\frac {90\,a^8\,b\,c\,d^9}{11}+\frac {1620\,a^7\,b^2\,c^2\,d^8}{11}+\frac {10080\,a^6\,b^3\,c^3\,d^7}{11}+\frac {26460\,a^5\,b^4\,c^4\,d^6}{11}+\frac {31752\,a^4\,b^5\,c^5\,d^5}{11}+\frac {17640\,a^3\,b^6\,c^6\,d^4}{11}+\frac {4320\,a^2\,b^7\,c^7\,d^3}{11}+\frac {405\,a\,b^8\,c^8\,d^2}{11}+\frac {10\,b^9\,c^9\,d}{11}\right )+a^9\,c^{10}\,x+\frac {b^9\,d^{10}\,x^{20}}{20}+\frac {3\,a^6\,c^7\,x^4\,\left (40\,a^3\,d^3+135\,a^2\,b\,c\,d^2+120\,a\,b^2\,c^2\,d+28\,b^3\,c^3\right )}{4}+\frac {3\,b^6\,d^7\,x^{17}\,\left (28\,a^3\,d^3+120\,a^2\,b\,c\,d^2+135\,a\,b^2\,c^2\,d+40\,b^3\,c^3\right )}{17}+\frac {a^8\,c^9\,x^2\,\left (10\,a\,d+9\,b\,c\right )}{2}+\frac {b^8\,d^9\,x^{19}\,\left (9\,a\,d+10\,b\,c\right )}{19}+3\,a^7\,c^8\,x^3\,\left (5\,a^2\,d^2+10\,a\,b\,c\,d+4\,b^2\,c^2\right )+\frac {b^7\,d^8\,x^{18}\,\left (4\,a^2\,d^2+10\,a\,b\,c\,d+5\,b^2\,c^2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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