Optimal. Leaf size=279 \[ \frac {(b c-a d)^{10} (a+b x)^{11}}{11 b^{11}}+\frac {5 d (b c-a d)^9 (a+b x)^{12}}{6 b^{11}}+\frac {45 d^2 (b c-a d)^8 (a+b x)^{13}}{13 b^{11}}+\frac {60 d^3 (b c-a d)^7 (a+b x)^{14}}{7 b^{11}}+\frac {14 d^4 (b c-a d)^6 (a+b x)^{15}}{b^{11}}+\frac {63 d^5 (b c-a d)^5 (a+b x)^{16}}{4 b^{11}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^{17}}{17 b^{11}}+\frac {20 d^7 (b c-a d)^3 (a+b x)^{18}}{3 b^{11}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^{19}}{19 b^{11}}+\frac {d^9 (b c-a d) (a+b x)^{20}}{2 b^{11}}+\frac {d^{10} (a+b x)^{21}}{21 b^{11}} \]
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Rubi [A]
time = 0.77, antiderivative size = 279, 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 {d^9 (a+b x)^{20} (b c-a d)}{2 b^{11}}+\frac {45 d^8 (a+b x)^{19} (b c-a d)^2}{19 b^{11}}+\frac {20 d^7 (a+b x)^{18} (b c-a d)^3}{3 b^{11}}+\frac {210 d^6 (a+b x)^{17} (b c-a d)^4}{17 b^{11}}+\frac {63 d^5 (a+b x)^{16} (b c-a d)^5}{4 b^{11}}+\frac {14 d^4 (a+b x)^{15} (b c-a d)^6}{b^{11}}+\frac {60 d^3 (a+b x)^{14} (b c-a d)^7}{7 b^{11}}+\frac {45 d^2 (a+b x)^{13} (b c-a d)^8}{13 b^{11}}+\frac {5 d (a+b x)^{12} (b c-a d)^9}{6 b^{11}}+\frac {(a+b x)^{11} (b c-a d)^{10}}{11 b^{11}}+\frac {d^{10} (a+b x)^{21}}{21 b^{11}} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (a+b x)^{10} (c+d x)^{10} \, dx &=\int \left (\frac {(b c-a d)^{10} (a+b x)^{10}}{b^{10}}+\frac {10 d (b c-a d)^9 (a+b x)^{11}}{b^{10}}+\frac {45 d^2 (b c-a d)^8 (a+b x)^{12}}{b^{10}}+\frac {120 d^3 (b c-a d)^7 (a+b x)^{13}}{b^{10}}+\frac {210 d^4 (b c-a d)^6 (a+b x)^{14}}{b^{10}}+\frac {252 d^5 (b c-a d)^5 (a+b x)^{15}}{b^{10}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^{16}}{b^{10}}+\frac {120 d^7 (b c-a d)^3 (a+b x)^{17}}{b^{10}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^{18}}{b^{10}}+\frac {10 d^9 (b c-a d) (a+b x)^{19}}{b^{10}}+\frac {d^{10} (a+b x)^{20}}{b^{10}}\right ) \, dx\\ &=\frac {(b c-a d)^{10} (a+b x)^{11}}{11 b^{11}}+\frac {5 d (b c-a d)^9 (a+b x)^{12}}{6 b^{11}}+\frac {45 d^2 (b c-a d)^8 (a+b x)^{13}}{13 b^{11}}+\frac {60 d^3 (b c-a d)^7 (a+b x)^{14}}{7 b^{11}}+\frac {14 d^4 (b c-a d)^6 (a+b x)^{15}}{b^{11}}+\frac {63 d^5 (b c-a d)^5 (a+b x)^{16}}{4 b^{11}}+\frac {210 d^6 (b c-a d)^4 (a+b x)^{17}}{17 b^{11}}+\frac {20 d^7 (b c-a d)^3 (a+b x)^{18}}{3 b^{11}}+\frac {45 d^8 (b c-a d)^2 (a+b x)^{19}}{19 b^{11}}+\frac {d^9 (b c-a d) (a+b x)^{20}}{2 b^{11}}+\frac {d^{10} (a+b x)^{21}}{21 b^{11}}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1539\) vs. \(2(279)=558\).
time = 0.12, size = 1539, normalized size = 5.52 \begin {gather*} a^{10} c^{10} x+5 a^9 c^9 (b c+a d) x^2+\frac {5}{3} a^8 c^8 \left (9 b^2 c^2+20 a b c d+9 a^2 d^2\right ) x^3+\frac {15}{2} a^7 c^7 \left (4 b^3 c^3+15 a b^2 c^2 d+15 a^2 b c d^2+4 a^3 d^3\right ) x^4+3 a^6 c^6 \left (14 b^4 c^4+80 a b^3 c^3 d+135 a^2 b^2 c^2 d^2+80 a^3 b c d^3+14 a^4 d^4\right ) x^5+2 a^5 c^5 \left (21 b^5 c^5+175 a b^4 c^4 d+450 a^2 b^3 c^3 d^2+450 a^3 b^2 c^2 d^3+175 a^4 b c d^4+21 a^5 d^5\right ) x^6+\frac {30}{7} a^4 c^4 \left (7 b^6 c^6+84 a b^5 c^5 d+315 a^2 b^4 c^4 d^2+480 a^3 b^3 c^3 d^3+315 a^4 b^2 c^2 d^4+84 a^5 b c d^5+7 a^6 d^6\right ) x^7+\frac {15}{2} a^3 c^3 \left (2 b^7 c^7+35 a b^6 c^6 d+189 a^2 b^5 c^5 d^2+420 a^3 b^4 c^4 d^3+420 a^4 b^3 c^3 d^4+189 a^5 b^2 c^2 d^5+35 a^6 b c d^6+2 a^7 d^7\right ) x^8+\frac {5}{3} a^2 c^2 \left (3 b^8 c^8+80 a b^7 c^7 d+630 a^2 b^6 c^6 d^2+2016 a^3 b^5 c^5 d^3+2940 a^4 b^4 c^4 d^4+2016 a^5 b^3 c^3 d^5+630 a^6 b^2 c^2 d^6+80 a^7 b c d^7+3 a^8 d^8\right ) x^9+a c \left (b^9 c^9+45 a b^8 c^8 d+540 a^2 b^7 c^7 d^2+2520 a^3 b^6 c^6 d^3+5292 a^4 b^5 c^5 d^4+5292 a^5 b^4 c^4 d^5+2520 a^6 b^3 c^3 d^6+540 a^7 b^2 c^2 d^7+45 a^8 b c d^8+a^9 d^9\right ) x^{10}+\frac {1}{11} \left (b^{10} c^{10}+100 a b^9 c^9 d+2025 a^2 b^8 c^8 d^2+14400 a^3 b^7 c^7 d^3+44100 a^4 b^6 c^6 d^4+63504 a^5 b^5 c^5 d^5+44100 a^6 b^4 c^4 d^6+14400 a^7 b^3 c^3 d^7+2025 a^8 b^2 c^2 d^8+100 a^9 b c d^9+a^{10} d^{10}\right ) x^{11}+\frac {5}{6} b d \left (b^9 c^9+45 a b^8 c^8 d+540 a^2 b^7 c^7 d^2+2520 a^3 b^6 c^6 d^3+5292 a^4 b^5 c^5 d^4+5292 a^5 b^4 c^4 d^5+2520 a^6 b^3 c^3 d^6+540 a^7 b^2 c^2 d^7+45 a^8 b c d^8+a^9 d^9\right ) x^{12}+\frac {15}{13} b^2 d^2 \left (3 b^8 c^8+80 a b^7 c^7 d+630 a^2 b^6 c^6 d^2+2016 a^3 b^5 c^5 d^3+2940 a^4 b^4 c^4 d^4+2016 a^5 b^3 c^3 d^5+630 a^6 b^2 c^2 d^6+80 a^7 b c d^7+3 a^8 d^8\right ) x^{13}+\frac {30}{7} b^3 d^3 \left (2 b^7 c^7+35 a b^6 c^6 d+189 a^2 b^5 c^5 d^2+420 a^3 b^4 c^4 d^3+420 a^4 b^3 c^3 d^4+189 a^5 b^2 c^2 d^5+35 a^6 b c d^6+2 a^7 d^7\right ) x^{14}+2 b^4 d^4 \left (7 b^6 c^6+84 a b^5 c^5 d+315 a^2 b^4 c^4 d^2+480 a^3 b^3 c^3 d^3+315 a^4 b^2 c^2 d^4+84 a^5 b c d^5+7 a^6 d^6\right ) x^{15}+\frac {3}{4} b^5 d^5 \left (21 b^5 c^5+175 a b^4 c^4 d+450 a^2 b^3 c^3 d^2+450 a^3 b^2 c^2 d^3+175 a^4 b c d^4+21 a^5 d^5\right ) x^{16}+\frac {15}{17} b^6 d^6 \left (14 b^4 c^4+80 a b^3 c^3 d+135 a^2 b^2 c^2 d^2+80 a^3 b c d^3+14 a^4 d^4\right ) x^{17}+\frac {5}{3} b^7 d^7 \left (4 b^3 c^3+15 a b^2 c^2 d+15 a^2 b c d^2+4 a^3 d^3\right ) x^{18}+\frac {5}{19} b^8 d^8 \left (9 b^2 c^2+20 a b c d+9 a^2 d^2\right ) x^{19}+\frac {1}{2} b^9 d^9 (b c+a d) x^{20}+\frac {1}{21} b^{10} d^{10} x^{21} \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. \(1590\) vs.
\(2(259)=518\).
time = 0.13, size = 1591, normalized size = 5.70
method | result | size |
norman | \(\text {Expression too large to display}\) | \(1572\) |
default | \(\text {Expression too large to display}\) | \(1591\) |
gosper | \(\text {Expression too large to display}\) | \(1834\) |
risch | \(\text {Expression too large to display}\) | \(1834\) |
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. 1581 vs.
\(2 (259) = 518\).
time = 0.28, size = 1581, normalized size = 5.67 \begin {gather*} \frac {1}{21} \, b^{10} d^{10} x^{21} + a^{10} c^{10} x + \frac {1}{2} \, {\left (b^{10} c d^{9} + a b^{9} d^{10}\right )} x^{20} + \frac {5}{19} \, {\left (9 \, b^{10} c^{2} d^{8} + 20 \, a b^{9} c d^{9} + 9 \, a^{2} b^{8} d^{10}\right )} x^{19} + \frac {5}{3} \, {\left (4 \, b^{10} c^{3} d^{7} + 15 \, a b^{9} c^{2} d^{8} + 15 \, a^{2} b^{8} c d^{9} + 4 \, a^{3} b^{7} d^{10}\right )} x^{18} + \frac {15}{17} \, {\left (14 \, b^{10} c^{4} d^{6} + 80 \, a b^{9} c^{3} d^{7} + 135 \, a^{2} b^{8} c^{2} d^{8} + 80 \, a^{3} b^{7} c d^{9} + 14 \, a^{4} b^{6} d^{10}\right )} x^{17} + \frac {3}{4} \, {\left (21 \, b^{10} c^{5} d^{5} + 175 \, a b^{9} c^{4} d^{6} + 450 \, a^{2} b^{8} c^{3} d^{7} + 450 \, a^{3} b^{7} c^{2} d^{8} + 175 \, a^{4} b^{6} c d^{9} + 21 \, a^{5} b^{5} d^{10}\right )} x^{16} + 2 \, {\left (7 \, b^{10} c^{6} d^{4} + 84 \, a b^{9} c^{5} d^{5} + 315 \, a^{2} b^{8} c^{4} d^{6} + 480 \, a^{3} b^{7} c^{3} d^{7} + 315 \, a^{4} b^{6} c^{2} d^{8} + 84 \, a^{5} b^{5} c d^{9} + 7 \, a^{6} b^{4} d^{10}\right )} x^{15} + \frac {30}{7} \, {\left (2 \, b^{10} c^{7} d^{3} + 35 \, a b^{9} c^{6} d^{4} + 189 \, a^{2} b^{8} c^{5} d^{5} + 420 \, a^{3} b^{7} c^{4} d^{6} + 420 \, a^{4} b^{6} c^{3} d^{7} + 189 \, a^{5} b^{5} c^{2} d^{8} + 35 \, a^{6} b^{4} c d^{9} + 2 \, a^{7} b^{3} d^{10}\right )} x^{14} + \frac {15}{13} \, {\left (3 \, b^{10} c^{8} d^{2} + 80 \, a b^{9} c^{7} d^{3} + 630 \, a^{2} b^{8} c^{6} d^{4} + 2016 \, a^{3} b^{7} c^{5} d^{5} + 2940 \, a^{4} b^{6} c^{4} d^{6} + 2016 \, a^{5} b^{5} c^{3} d^{7} + 630 \, a^{6} b^{4} c^{2} d^{8} + 80 \, a^{7} b^{3} c d^{9} + 3 \, a^{8} b^{2} d^{10}\right )} x^{13} + \frac {5}{6} \, {\left (b^{10} c^{9} d + 45 \, a b^{9} c^{8} d^{2} + 540 \, a^{2} b^{8} c^{7} d^{3} + 2520 \, a^{3} b^{7} c^{6} d^{4} + 5292 \, a^{4} b^{6} c^{5} d^{5} + 5292 \, a^{5} b^{5} c^{4} d^{6} + 2520 \, a^{6} b^{4} c^{3} d^{7} + 540 \, a^{7} b^{3} c^{2} d^{8} + 45 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x^{12} + \frac {1}{11} \, {\left (b^{10} c^{10} + 100 \, a b^{9} c^{9} d + 2025 \, a^{2} b^{8} c^{8} d^{2} + 14400 \, a^{3} b^{7} c^{7} d^{3} + 44100 \, a^{4} b^{6} c^{6} d^{4} + 63504 \, a^{5} b^{5} c^{5} d^{5} + 44100 \, a^{6} b^{4} c^{4} d^{6} + 14400 \, a^{7} b^{3} c^{3} d^{7} + 2025 \, a^{8} b^{2} c^{2} d^{8} + 100 \, a^{9} b c d^{9} + a^{10} d^{10}\right )} x^{11} + {\left (a b^{9} c^{10} + 45 \, a^{2} b^{8} c^{9} d + 540 \, a^{3} b^{7} c^{8} d^{2} + 2520 \, a^{4} b^{6} c^{7} d^{3} + 5292 \, a^{5} b^{5} c^{6} d^{4} + 5292 \, a^{6} b^{4} c^{5} d^{5} + 2520 \, a^{7} b^{3} c^{4} d^{6} + 540 \, a^{8} b^{2} c^{3} d^{7} + 45 \, a^{9} b c^{2} d^{8} + a^{10} c d^{9}\right )} x^{10} + \frac {5}{3} \, {\left (3 \, a^{2} b^{8} c^{10} + 80 \, a^{3} b^{7} c^{9} d + 630 \, a^{4} b^{6} c^{8} d^{2} + 2016 \, a^{5} b^{5} c^{7} d^{3} + 2940 \, a^{6} b^{4} c^{6} d^{4} + 2016 \, a^{7} b^{3} c^{5} d^{5} + 630 \, a^{8} b^{2} c^{4} d^{6} + 80 \, a^{9} b c^{3} d^{7} + 3 \, a^{10} c^{2} d^{8}\right )} x^{9} + \frac {15}{2} \, {\left (2 \, a^{3} b^{7} c^{10} + 35 \, a^{4} b^{6} c^{9} d + 189 \, a^{5} b^{5} c^{8} d^{2} + 420 \, a^{6} b^{4} c^{7} d^{3} + 420 \, a^{7} b^{3} c^{6} d^{4} + 189 \, a^{8} b^{2} c^{5} d^{5} + 35 \, a^{9} b c^{4} d^{6} + 2 \, a^{10} c^{3} d^{7}\right )} x^{8} + \frac {30}{7} \, {\left (7 \, a^{4} b^{6} c^{10} + 84 \, a^{5} b^{5} c^{9} d + 315 \, a^{6} b^{4} c^{8} d^{2} + 480 \, a^{7} b^{3} c^{7} d^{3} + 315 \, a^{8} b^{2} c^{6} d^{4} + 84 \, a^{9} b c^{5} d^{5} + 7 \, a^{10} c^{4} d^{6}\right )} x^{7} + 2 \, {\left (21 \, a^{5} b^{5} c^{10} + 175 \, a^{6} b^{4} c^{9} d + 450 \, a^{7} b^{3} c^{8} d^{2} + 450 \, a^{8} b^{2} c^{7} d^{3} + 175 \, a^{9} b c^{6} d^{4} + 21 \, a^{10} c^{5} d^{5}\right )} x^{6} + 3 \, {\left (14 \, a^{6} b^{4} c^{10} + 80 \, a^{7} b^{3} c^{9} d + 135 \, a^{8} b^{2} c^{8} d^{2} + 80 \, a^{9} b c^{7} d^{3} + 14 \, a^{10} c^{6} d^{4}\right )} x^{5} + \frac {15}{2} \, {\left (4 \, a^{7} b^{3} c^{10} + 15 \, a^{8} b^{2} c^{9} d + 15 \, a^{9} b c^{8} d^{2} + 4 \, a^{10} c^{7} d^{3}\right )} x^{4} + \frac {5}{3} \, {\left (9 \, a^{8} b^{2} c^{10} + 20 \, a^{9} b c^{9} d + 9 \, a^{10} c^{8} d^{2}\right )} x^{3} + 5 \, {\left (a^{9} b c^{10} + a^{10} 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. 1581 vs.
\(2 (259) = 518\).
time = 0.61, size = 1581, normalized size = 5.67 \begin {gather*} \frac {1}{21} \, b^{10} d^{10} x^{21} + a^{10} c^{10} x + \frac {1}{2} \, {\left (b^{10} c d^{9} + a b^{9} d^{10}\right )} x^{20} + \frac {5}{19} \, {\left (9 \, b^{10} c^{2} d^{8} + 20 \, a b^{9} c d^{9} + 9 \, a^{2} b^{8} d^{10}\right )} x^{19} + \frac {5}{3} \, {\left (4 \, b^{10} c^{3} d^{7} + 15 \, a b^{9} c^{2} d^{8} + 15 \, a^{2} b^{8} c d^{9} + 4 \, a^{3} b^{7} d^{10}\right )} x^{18} + \frac {15}{17} \, {\left (14 \, b^{10} c^{4} d^{6} + 80 \, a b^{9} c^{3} d^{7} + 135 \, a^{2} b^{8} c^{2} d^{8} + 80 \, a^{3} b^{7} c d^{9} + 14 \, a^{4} b^{6} d^{10}\right )} x^{17} + \frac {3}{4} \, {\left (21 \, b^{10} c^{5} d^{5} + 175 \, a b^{9} c^{4} d^{6} + 450 \, a^{2} b^{8} c^{3} d^{7} + 450 \, a^{3} b^{7} c^{2} d^{8} + 175 \, a^{4} b^{6} c d^{9} + 21 \, a^{5} b^{5} d^{10}\right )} x^{16} + 2 \, {\left (7 \, b^{10} c^{6} d^{4} + 84 \, a b^{9} c^{5} d^{5} + 315 \, a^{2} b^{8} c^{4} d^{6} + 480 \, a^{3} b^{7} c^{3} d^{7} + 315 \, a^{4} b^{6} c^{2} d^{8} + 84 \, a^{5} b^{5} c d^{9} + 7 \, a^{6} b^{4} d^{10}\right )} x^{15} + \frac {30}{7} \, {\left (2 \, b^{10} c^{7} d^{3} + 35 \, a b^{9} c^{6} d^{4} + 189 \, a^{2} b^{8} c^{5} d^{5} + 420 \, a^{3} b^{7} c^{4} d^{6} + 420 \, a^{4} b^{6} c^{3} d^{7} + 189 \, a^{5} b^{5} c^{2} d^{8} + 35 \, a^{6} b^{4} c d^{9} + 2 \, a^{7} b^{3} d^{10}\right )} x^{14} + \frac {15}{13} \, {\left (3 \, b^{10} c^{8} d^{2} + 80 \, a b^{9} c^{7} d^{3} + 630 \, a^{2} b^{8} c^{6} d^{4} + 2016 \, a^{3} b^{7} c^{5} d^{5} + 2940 \, a^{4} b^{6} c^{4} d^{6} + 2016 \, a^{5} b^{5} c^{3} d^{7} + 630 \, a^{6} b^{4} c^{2} d^{8} + 80 \, a^{7} b^{3} c d^{9} + 3 \, a^{8} b^{2} d^{10}\right )} x^{13} + \frac {5}{6} \, {\left (b^{10} c^{9} d + 45 \, a b^{9} c^{8} d^{2} + 540 \, a^{2} b^{8} c^{7} d^{3} + 2520 \, a^{3} b^{7} c^{6} d^{4} + 5292 \, a^{4} b^{6} c^{5} d^{5} + 5292 \, a^{5} b^{5} c^{4} d^{6} + 2520 \, a^{6} b^{4} c^{3} d^{7} + 540 \, a^{7} b^{3} c^{2} d^{8} + 45 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x^{12} + \frac {1}{11} \, {\left (b^{10} c^{10} + 100 \, a b^{9} c^{9} d + 2025 \, a^{2} b^{8} c^{8} d^{2} + 14400 \, a^{3} b^{7} c^{7} d^{3} + 44100 \, a^{4} b^{6} c^{6} d^{4} + 63504 \, a^{5} b^{5} c^{5} d^{5} + 44100 \, a^{6} b^{4} c^{4} d^{6} + 14400 \, a^{7} b^{3} c^{3} d^{7} + 2025 \, a^{8} b^{2} c^{2} d^{8} + 100 \, a^{9} b c d^{9} + a^{10} d^{10}\right )} x^{11} + {\left (a b^{9} c^{10} + 45 \, a^{2} b^{8} c^{9} d + 540 \, a^{3} b^{7} c^{8} d^{2} + 2520 \, a^{4} b^{6} c^{7} d^{3} + 5292 \, a^{5} b^{5} c^{6} d^{4} + 5292 \, a^{6} b^{4} c^{5} d^{5} + 2520 \, a^{7} b^{3} c^{4} d^{6} + 540 \, a^{8} b^{2} c^{3} d^{7} + 45 \, a^{9} b c^{2} d^{8} + a^{10} c d^{9}\right )} x^{10} + \frac {5}{3} \, {\left (3 \, a^{2} b^{8} c^{10} + 80 \, a^{3} b^{7} c^{9} d + 630 \, a^{4} b^{6} c^{8} d^{2} + 2016 \, a^{5} b^{5} c^{7} d^{3} + 2940 \, a^{6} b^{4} c^{6} d^{4} + 2016 \, a^{7} b^{3} c^{5} d^{5} + 630 \, a^{8} b^{2} c^{4} d^{6} + 80 \, a^{9} b c^{3} d^{7} + 3 \, a^{10} c^{2} d^{8}\right )} x^{9} + \frac {15}{2} \, {\left (2 \, a^{3} b^{7} c^{10} + 35 \, a^{4} b^{6} c^{9} d + 189 \, a^{5} b^{5} c^{8} d^{2} + 420 \, a^{6} b^{4} c^{7} d^{3} + 420 \, a^{7} b^{3} c^{6} d^{4} + 189 \, a^{8} b^{2} c^{5} d^{5} + 35 \, a^{9} b c^{4} d^{6} + 2 \, a^{10} c^{3} d^{7}\right )} x^{8} + \frac {30}{7} \, {\left (7 \, a^{4} b^{6} c^{10} + 84 \, a^{5} b^{5} c^{9} d + 315 \, a^{6} b^{4} c^{8} d^{2} + 480 \, a^{7} b^{3} c^{7} d^{3} + 315 \, a^{8} b^{2} c^{6} d^{4} + 84 \, a^{9} b c^{5} d^{5} + 7 \, a^{10} c^{4} d^{6}\right )} x^{7} + 2 \, {\left (21 \, a^{5} b^{5} c^{10} + 175 \, a^{6} b^{4} c^{9} d + 450 \, a^{7} b^{3} c^{8} d^{2} + 450 \, a^{8} b^{2} c^{7} d^{3} + 175 \, a^{9} b c^{6} d^{4} + 21 \, a^{10} c^{5} d^{5}\right )} x^{6} + 3 \, {\left (14 \, a^{6} b^{4} c^{10} + 80 \, a^{7} b^{3} c^{9} d + 135 \, a^{8} b^{2} c^{8} d^{2} + 80 \, a^{9} b c^{7} d^{3} + 14 \, a^{10} c^{6} d^{4}\right )} x^{5} + \frac {15}{2} \, {\left (4 \, a^{7} b^{3} c^{10} + 15 \, a^{8} b^{2} c^{9} d + 15 \, a^{9} b c^{8} d^{2} + 4 \, a^{10} c^{7} d^{3}\right )} x^{4} + \frac {5}{3} \, {\left (9 \, a^{8} b^{2} c^{10} + 20 \, a^{9} b c^{9} d + 9 \, a^{10} c^{8} d^{2}\right )} x^{3} + 5 \, {\left (a^{9} b c^{10} + a^{10} 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. 1775 vs.
\(2 (257) = 514\).
time = 0.12, size = 1775, normalized size = 6.36 \begin {gather*} a^{10} c^{10} x + \frac {b^{10} d^{10} x^{21}}{21} + x^{20} \left (\frac {a b^{9} d^{10}}{2} + \frac {b^{10} c d^{9}}{2}\right ) + x^{19} \cdot \left (\frac {45 a^{2} b^{8} d^{10}}{19} + \frac {100 a b^{9} c d^{9}}{19} + \frac {45 b^{10} c^{2} d^{8}}{19}\right ) + x^{18} \cdot \left (\frac {20 a^{3} b^{7} d^{10}}{3} + 25 a^{2} b^{8} c d^{9} + 25 a b^{9} c^{2} d^{8} + \frac {20 b^{10} c^{3} d^{7}}{3}\right ) + x^{17} \cdot \left (\frac {210 a^{4} b^{6} d^{10}}{17} + \frac {1200 a^{3} b^{7} c d^{9}}{17} + \frac {2025 a^{2} b^{8} c^{2} d^{8}}{17} + \frac {1200 a b^{9} c^{3} d^{7}}{17} + \frac {210 b^{10} c^{4} d^{6}}{17}\right ) + x^{16} \cdot \left (\frac {63 a^{5} b^{5} d^{10}}{4} + \frac {525 a^{4} b^{6} c d^{9}}{4} + \frac {675 a^{3} b^{7} c^{2} d^{8}}{2} + \frac {675 a^{2} b^{8} c^{3} d^{7}}{2} + \frac {525 a b^{9} c^{4} d^{6}}{4} + \frac {63 b^{10} c^{5} d^{5}}{4}\right ) + x^{15} \cdot \left (14 a^{6} b^{4} d^{10} + 168 a^{5} b^{5} c d^{9} + 630 a^{4} b^{6} c^{2} d^{8} + 960 a^{3} b^{7} c^{3} d^{7} + 630 a^{2} b^{8} c^{4} d^{6} + 168 a b^{9} c^{5} d^{5} + 14 b^{10} c^{6} d^{4}\right ) + x^{14} \cdot \left (\frac {60 a^{7} b^{3} d^{10}}{7} + 150 a^{6} b^{4} c d^{9} + 810 a^{5} b^{5} c^{2} d^{8} + 1800 a^{4} b^{6} c^{3} d^{7} + 1800 a^{3} b^{7} c^{4} d^{6} + 810 a^{2} b^{8} c^{5} d^{5} + 150 a b^{9} c^{6} d^{4} + \frac {60 b^{10} c^{7} d^{3}}{7}\right ) + x^{13} \cdot \left (\frac {45 a^{8} b^{2} d^{10}}{13} + \frac {1200 a^{7} b^{3} c d^{9}}{13} + \frac {9450 a^{6} b^{4} c^{2} d^{8}}{13} + \frac {30240 a^{5} b^{5} c^{3} d^{7}}{13} + \frac {44100 a^{4} b^{6} c^{4} d^{6}}{13} + \frac {30240 a^{3} b^{7} c^{5} d^{5}}{13} + \frac {9450 a^{2} b^{8} c^{6} d^{4}}{13} + \frac {1200 a b^{9} c^{7} d^{3}}{13} + \frac {45 b^{10} c^{8} d^{2}}{13}\right ) + x^{12} \cdot \left (\frac {5 a^{9} b d^{10}}{6} + \frac {75 a^{8} b^{2} c d^{9}}{2} + 450 a^{7} b^{3} c^{2} d^{8} + 2100 a^{6} b^{4} c^{3} d^{7} + 4410 a^{5} b^{5} c^{4} d^{6} + 4410 a^{4} b^{6} c^{5} d^{5} + 2100 a^{3} b^{7} c^{6} d^{4} + 450 a^{2} b^{8} c^{7} d^{3} + \frac {75 a b^{9} c^{8} d^{2}}{2} + \frac {5 b^{10} c^{9} d}{6}\right ) + x^{11} \left (\frac {a^{10} d^{10}}{11} + \frac {100 a^{9} b c d^{9}}{11} + \frac {2025 a^{8} b^{2} c^{2} d^{8}}{11} + \frac {14400 a^{7} b^{3} c^{3} d^{7}}{11} + \frac {44100 a^{6} b^{4} c^{4} d^{6}}{11} + \frac {63504 a^{5} b^{5} c^{5} d^{5}}{11} + \frac {44100 a^{4} b^{6} c^{6} d^{4}}{11} + \frac {14400 a^{3} b^{7} c^{7} d^{3}}{11} + \frac {2025 a^{2} b^{8} c^{8} d^{2}}{11} + \frac {100 a b^{9} c^{9} d}{11} + \frac {b^{10} c^{10}}{11}\right ) + x^{10} \left (a^{10} c d^{9} + 45 a^{9} b c^{2} d^{8} + 540 a^{8} b^{2} c^{3} d^{7} + 2520 a^{7} b^{3} c^{4} d^{6} + 5292 a^{6} b^{4} c^{5} d^{5} + 5292 a^{5} b^{5} c^{6} d^{4} + 2520 a^{4} b^{6} c^{7} d^{3} + 540 a^{3} b^{7} c^{8} d^{2} + 45 a^{2} b^{8} c^{9} d + a b^{9} c^{10}\right ) + x^{9} \cdot \left (5 a^{10} c^{2} d^{8} + \frac {400 a^{9} b c^{3} d^{7}}{3} + 1050 a^{8} b^{2} c^{4} d^{6} + 3360 a^{7} b^{3} c^{5} d^{5} + 4900 a^{6} b^{4} c^{6} d^{4} + 3360 a^{5} b^{5} c^{7} d^{3} + 1050 a^{4} b^{6} c^{8} d^{2} + \frac {400 a^{3} b^{7} c^{9} d}{3} + 5 a^{2} b^{8} c^{10}\right ) + x^{8} \cdot \left (15 a^{10} c^{3} d^{7} + \frac {525 a^{9} b c^{4} d^{6}}{2} + \frac {2835 a^{8} b^{2} c^{5} d^{5}}{2} + 3150 a^{7} b^{3} c^{6} d^{4} + 3150 a^{6} b^{4} c^{7} d^{3} + \frac {2835 a^{5} b^{5} c^{8} d^{2}}{2} + \frac {525 a^{4} b^{6} c^{9} d}{2} + 15 a^{3} b^{7} c^{10}\right ) + x^{7} \cdot \left (30 a^{10} c^{4} d^{6} + 360 a^{9} b c^{5} d^{5} + 1350 a^{8} b^{2} c^{6} d^{4} + \frac {14400 a^{7} b^{3} c^{7} d^{3}}{7} + 1350 a^{6} b^{4} c^{8} d^{2} + 360 a^{5} b^{5} c^{9} d + 30 a^{4} b^{6} c^{10}\right ) + x^{6} \cdot \left (42 a^{10} c^{5} d^{5} + 350 a^{9} b c^{6} d^{4} + 900 a^{8} b^{2} c^{7} d^{3} + 900 a^{7} b^{3} c^{8} d^{2} + 350 a^{6} b^{4} c^{9} d + 42 a^{5} b^{5} c^{10}\right ) + x^{5} \cdot \left (42 a^{10} c^{6} d^{4} + 240 a^{9} b c^{7} d^{3} + 405 a^{8} b^{2} c^{8} d^{2} + 240 a^{7} b^{3} c^{9} d + 42 a^{6} b^{4} c^{10}\right ) + x^{4} \cdot \left (30 a^{10} c^{7} d^{3} + \frac {225 a^{9} b c^{8} d^{2}}{2} + \frac {225 a^{8} b^{2} c^{9} d}{2} + 30 a^{7} b^{3} c^{10}\right ) + x^{3} \cdot \left (15 a^{10} c^{8} d^{2} + \frac {100 a^{9} b c^{9} d}{3} + 15 a^{8} b^{2} c^{10}\right ) + x^{2} \cdot \left (5 a^{10} c^{9} d + 5 a^{9} b c^{10}\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. 1833 vs.
\(2 (259) = 518\).
time = 1.16, size = 1833, normalized size = 6.57 \begin {gather*} \frac {1}{21} \, b^{10} d^{10} x^{21} + \frac {1}{2} \, b^{10} c d^{9} x^{20} + \frac {1}{2} \, a b^{9} d^{10} x^{20} + \frac {45}{19} \, b^{10} c^{2} d^{8} x^{19} + \frac {100}{19} \, a b^{9} c d^{9} x^{19} + \frac {45}{19} \, a^{2} b^{8} d^{10} x^{19} + \frac {20}{3} \, b^{10} c^{3} d^{7} x^{18} + 25 \, a b^{9} c^{2} d^{8} x^{18} + 25 \, a^{2} b^{8} c d^{9} x^{18} + \frac {20}{3} \, a^{3} b^{7} d^{10} x^{18} + \frac {210}{17} \, b^{10} c^{4} d^{6} x^{17} + \frac {1200}{17} \, a b^{9} c^{3} d^{7} x^{17} + \frac {2025}{17} \, a^{2} b^{8} c^{2} d^{8} x^{17} + \frac {1200}{17} \, a^{3} b^{7} c d^{9} x^{17} + \frac {210}{17} \, a^{4} b^{6} d^{10} x^{17} + \frac {63}{4} \, b^{10} c^{5} d^{5} x^{16} + \frac {525}{4} \, a b^{9} c^{4} d^{6} x^{16} + \frac {675}{2} \, a^{2} b^{8} c^{3} d^{7} x^{16} + \frac {675}{2} \, a^{3} b^{7} c^{2} d^{8} x^{16} + \frac {525}{4} \, a^{4} b^{6} c d^{9} x^{16} + \frac {63}{4} \, a^{5} b^{5} d^{10} x^{16} + 14 \, b^{10} c^{6} d^{4} x^{15} + 168 \, a b^{9} c^{5} d^{5} x^{15} + 630 \, a^{2} b^{8} c^{4} d^{6} x^{15} + 960 \, a^{3} b^{7} c^{3} d^{7} x^{15} + 630 \, a^{4} b^{6} c^{2} d^{8} x^{15} + 168 \, a^{5} b^{5} c d^{9} x^{15} + 14 \, a^{6} b^{4} d^{10} x^{15} + \frac {60}{7} \, b^{10} c^{7} d^{3} x^{14} + 150 \, a b^{9} c^{6} d^{4} x^{14} + 810 \, a^{2} b^{8} c^{5} d^{5} x^{14} + 1800 \, a^{3} b^{7} c^{4} d^{6} x^{14} + 1800 \, a^{4} b^{6} c^{3} d^{7} x^{14} + 810 \, a^{5} b^{5} c^{2} d^{8} x^{14} + 150 \, a^{6} b^{4} c d^{9} x^{14} + \frac {60}{7} \, a^{7} b^{3} d^{10} x^{14} + \frac {45}{13} \, b^{10} c^{8} d^{2} x^{13} + \frac {1200}{13} \, a b^{9} c^{7} d^{3} x^{13} + \frac {9450}{13} \, a^{2} b^{8} c^{6} d^{4} x^{13} + \frac {30240}{13} \, a^{3} b^{7} c^{5} d^{5} x^{13} + \frac {44100}{13} \, a^{4} b^{6} c^{4} d^{6} x^{13} + \frac {30240}{13} \, a^{5} b^{5} c^{3} d^{7} x^{13} + \frac {9450}{13} \, a^{6} b^{4} c^{2} d^{8} x^{13} + \frac {1200}{13} \, a^{7} b^{3} c d^{9} x^{13} + \frac {45}{13} \, a^{8} b^{2} d^{10} x^{13} + \frac {5}{6} \, b^{10} c^{9} d x^{12} + \frac {75}{2} \, a b^{9} c^{8} d^{2} x^{12} + 450 \, a^{2} b^{8} c^{7} d^{3} x^{12} + 2100 \, a^{3} b^{7} c^{6} d^{4} x^{12} + 4410 \, a^{4} b^{6} c^{5} d^{5} x^{12} + 4410 \, a^{5} b^{5} c^{4} d^{6} x^{12} + 2100 \, a^{6} b^{4} c^{3} d^{7} x^{12} + 450 \, a^{7} b^{3} c^{2} d^{8} x^{12} + \frac {75}{2} \, a^{8} b^{2} c d^{9} x^{12} + \frac {5}{6} \, a^{9} b d^{10} x^{12} + \frac {1}{11} \, b^{10} c^{10} x^{11} + \frac {100}{11} \, a b^{9} c^{9} d x^{11} + \frac {2025}{11} \, a^{2} b^{8} c^{8} d^{2} x^{11} + \frac {14400}{11} \, a^{3} b^{7} c^{7} d^{3} x^{11} + \frac {44100}{11} \, a^{4} b^{6} c^{6} d^{4} x^{11} + \frac {63504}{11} \, a^{5} b^{5} c^{5} d^{5} x^{11} + \frac {44100}{11} \, a^{6} b^{4} c^{4} d^{6} x^{11} + \frac {14400}{11} \, a^{7} b^{3} c^{3} d^{7} x^{11} + \frac {2025}{11} \, a^{8} b^{2} c^{2} d^{8} x^{11} + \frac {100}{11} \, a^{9} b c d^{9} x^{11} + \frac {1}{11} \, a^{10} d^{10} x^{11} + a b^{9} c^{10} x^{10} + 45 \, a^{2} b^{8} c^{9} d x^{10} + 540 \, a^{3} b^{7} c^{8} d^{2} x^{10} + 2520 \, a^{4} b^{6} c^{7} d^{3} x^{10} + 5292 \, a^{5} b^{5} c^{6} d^{4} x^{10} + 5292 \, a^{6} b^{4} c^{5} d^{5} x^{10} + 2520 \, a^{7} b^{3} c^{4} d^{6} x^{10} + 540 \, a^{8} b^{2} c^{3} d^{7} x^{10} + 45 \, a^{9} b c^{2} d^{8} x^{10} + a^{10} c d^{9} x^{10} + 5 \, a^{2} b^{8} c^{10} x^{9} + \frac {400}{3} \, a^{3} b^{7} c^{9} d x^{9} + 1050 \, a^{4} b^{6} c^{8} d^{2} x^{9} + 3360 \, a^{5} b^{5} c^{7} d^{3} x^{9} + 4900 \, a^{6} b^{4} c^{6} d^{4} x^{9} + 3360 \, a^{7} b^{3} c^{5} d^{5} x^{9} + 1050 \, a^{8} b^{2} c^{4} d^{6} x^{9} + \frac {400}{3} \, a^{9} b c^{3} d^{7} x^{9} + 5 \, a^{10} c^{2} d^{8} x^{9} + 15 \, a^{3} b^{7} c^{10} x^{8} + \frac {525}{2} \, a^{4} b^{6} c^{9} d x^{8} + \frac {2835}{2} \, a^{5} b^{5} c^{8} d^{2} x^{8} + 3150 \, a^{6} b^{4} c^{7} d^{3} x^{8} + 3150 \, a^{7} b^{3} c^{6} d^{4} x^{8} + \frac {2835}{2} \, a^{8} b^{2} c^{5} d^{5} x^{8} + \frac {525}{2} \, a^{9} b c^{4} d^{6} x^{8} + 15 \, a^{10} c^{3} d^{7} x^{8} + 30 \, a^{4} b^{6} c^{10} x^{7} + 360 \, a^{5} b^{5} c^{9} d x^{7} + 1350 \, a^{6} b^{4} c^{8} d^{2} x^{7} + \frac {14400}{7} \, a^{7} b^{3} c^{7} d^{3} x^{7} + 1350 \, a^{8} b^{2} c^{6} d^{4} x^{7} + 360 \, a^{9} b c^{5} d^{5} x^{7} + 30 \, a^{10} c^{4} d^{6} x^{7} + 42 \, a^{5} b^{5} c^{10} x^{6} + 350 \, a^{6} b^{4} c^{9} d x^{6} + 900 \, a^{7} b^{3} c^{8} d^{2} x^{6} + 900 \, a^{8} b^{2} c^{7} d^{3} x^{6} + 350 \, a^{9} b c^{6} d^{4} x^{6} + 42 \, a^{10} c^{5} d^{5} x^{6} + 42 \, a^{6} b^{4} c^{10} x^{5} + 240 \, a^{7} b^{3} c^{9} d x^{5} + 405 \, a^{8} b^{2} c^{8} d^{2} x^{5} + 240 \, a^{9} b c^{7} d^{3} x^{5} + 42 \, a^{10} c^{6} d^{4} x^{5} + 30 \, a^{7} b^{3} c^{10} x^{4} + \frac {225}{2} \, a^{8} b^{2} c^{9} d x^{4} + \frac {225}{2} \, a^{9} b c^{8} d^{2} x^{4} + 30 \, a^{10} c^{7} d^{3} x^{4} + 15 \, a^{8} b^{2} c^{10} x^{3} + \frac {100}{3} \, a^{9} b c^{9} d x^{3} + 15 \, a^{10} c^{8} d^{2} x^{3} + 5 \, a^{9} b c^{10} x^{2} + 5 \, a^{10} c^{9} d x^{2} + a^{10} c^{10} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.69, size = 1549, normalized size = 5.55 \begin {gather*} x^7\,\left (30\,a^{10}\,c^4\,d^6+360\,a^9\,b\,c^5\,d^5+1350\,a^8\,b^2\,c^6\,d^4+\frac {14400\,a^7\,b^3\,c^7\,d^3}{7}+1350\,a^6\,b^4\,c^8\,d^2+360\,a^5\,b^5\,c^9\,d+30\,a^4\,b^6\,c^{10}\right )+x^{15}\,\left (14\,a^6\,b^4\,d^{10}+168\,a^5\,b^5\,c\,d^9+630\,a^4\,b^6\,c^2\,d^8+960\,a^3\,b^7\,c^3\,d^7+630\,a^2\,b^8\,c^4\,d^6+168\,a\,b^9\,c^5\,d^5+14\,b^{10}\,c^6\,d^4\right )+x^5\,\left (42\,a^{10}\,c^6\,d^4+240\,a^9\,b\,c^7\,d^3+405\,a^8\,b^2\,c^8\,d^2+240\,a^7\,b^3\,c^9\,d+42\,a^6\,b^4\,c^{10}\right )+x^{17}\,\left (\frac {210\,a^4\,b^6\,d^{10}}{17}+\frac {1200\,a^3\,b^7\,c\,d^9}{17}+\frac {2025\,a^2\,b^8\,c^2\,d^8}{17}+\frac {1200\,a\,b^9\,c^3\,d^7}{17}+\frac {210\,b^{10}\,c^4\,d^6}{17}\right )+x^{11}\,\left (\frac {a^{10}\,d^{10}}{11}+\frac {100\,a^9\,b\,c\,d^9}{11}+\frac {2025\,a^8\,b^2\,c^2\,d^8}{11}+\frac {14400\,a^7\,b^3\,c^3\,d^7}{11}+\frac {44100\,a^6\,b^4\,c^4\,d^6}{11}+\frac {63504\,a^5\,b^5\,c^5\,d^5}{11}+\frac {44100\,a^4\,b^6\,c^6\,d^4}{11}+\frac {14400\,a^3\,b^7\,c^7\,d^3}{11}+\frac {2025\,a^2\,b^8\,c^8\,d^2}{11}+\frac {100\,a\,b^9\,c^9\,d}{11}+\frac {b^{10}\,c^{10}}{11}\right )+x^8\,\left (15\,a^{10}\,c^3\,d^7+\frac {525\,a^9\,b\,c^4\,d^6}{2}+\frac {2835\,a^8\,b^2\,c^5\,d^5}{2}+3150\,a^7\,b^3\,c^6\,d^4+3150\,a^6\,b^4\,c^7\,d^3+\frac {2835\,a^5\,b^5\,c^8\,d^2}{2}+\frac {525\,a^4\,b^6\,c^9\,d}{2}+15\,a^3\,b^7\,c^{10}\right )+x^{14}\,\left (\frac {60\,a^7\,b^3\,d^{10}}{7}+150\,a^6\,b^4\,c\,d^9+810\,a^5\,b^5\,c^2\,d^8+1800\,a^4\,b^6\,c^3\,d^7+1800\,a^3\,b^7\,c^4\,d^6+810\,a^2\,b^8\,c^5\,d^5+150\,a\,b^9\,c^6\,d^4+\frac {60\,b^{10}\,c^7\,d^3}{7}\right )+x^{10}\,\left (a^{10}\,c\,d^9+45\,a^9\,b\,c^2\,d^8+540\,a^8\,b^2\,c^3\,d^7+2520\,a^7\,b^3\,c^4\,d^6+5292\,a^6\,b^4\,c^5\,d^5+5292\,a^5\,b^5\,c^6\,d^4+2520\,a^4\,b^6\,c^7\,d^3+540\,a^3\,b^7\,c^8\,d^2+45\,a^2\,b^8\,c^9\,d+a\,b^9\,c^{10}\right )+x^{12}\,\left (\frac {5\,a^9\,b\,d^{10}}{6}+\frac {75\,a^8\,b^2\,c\,d^9}{2}+450\,a^7\,b^3\,c^2\,d^8+2100\,a^6\,b^4\,c^3\,d^7+4410\,a^5\,b^5\,c^4\,d^6+4410\,a^4\,b^6\,c^5\,d^5+2100\,a^3\,b^7\,c^6\,d^4+450\,a^2\,b^8\,c^7\,d^3+\frac {75\,a\,b^9\,c^8\,d^2}{2}+\frac {5\,b^{10}\,c^9\,d}{6}\right )+x^6\,\left (42\,a^{10}\,c^5\,d^5+350\,a^9\,b\,c^6\,d^4+900\,a^8\,b^2\,c^7\,d^3+900\,a^7\,b^3\,c^8\,d^2+350\,a^6\,b^4\,c^9\,d+42\,a^5\,b^5\,c^{10}\right )+x^{16}\,\left (\frac {63\,a^5\,b^5\,d^{10}}{4}+\frac {525\,a^4\,b^6\,c\,d^9}{4}+\frac {675\,a^3\,b^7\,c^2\,d^8}{2}+\frac {675\,a^2\,b^8\,c^3\,d^7}{2}+\frac {525\,a\,b^9\,c^4\,d^6}{4}+\frac {63\,b^{10}\,c^5\,d^5}{4}\right )+x^9\,\left (5\,a^{10}\,c^2\,d^8+\frac {400\,a^9\,b\,c^3\,d^7}{3}+1050\,a^8\,b^2\,c^4\,d^6+3360\,a^7\,b^3\,c^5\,d^5+4900\,a^6\,b^4\,c^6\,d^4+3360\,a^5\,b^5\,c^7\,d^3+1050\,a^4\,b^6\,c^8\,d^2+\frac {400\,a^3\,b^7\,c^9\,d}{3}+5\,a^2\,b^8\,c^{10}\right )+x^{13}\,\left (\frac {45\,a^8\,b^2\,d^{10}}{13}+\frac {1200\,a^7\,b^3\,c\,d^9}{13}+\frac {9450\,a^6\,b^4\,c^2\,d^8}{13}+\frac {30240\,a^5\,b^5\,c^3\,d^7}{13}+\frac {44100\,a^4\,b^6\,c^4\,d^6}{13}+\frac {30240\,a^3\,b^7\,c^5\,d^5}{13}+\frac {9450\,a^2\,b^8\,c^6\,d^4}{13}+\frac {1200\,a\,b^9\,c^7\,d^3}{13}+\frac {45\,b^{10}\,c^8\,d^2}{13}\right )+a^{10}\,c^{10}\,x+\frac {b^{10}\,d^{10}\,x^{21}}{21}+\frac {15\,a^7\,c^7\,x^4\,\left (4\,a^3\,d^3+15\,a^2\,b\,c\,d^2+15\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right )}{2}+\frac {5\,b^7\,d^7\,x^{18}\,\left (4\,a^3\,d^3+15\,a^2\,b\,c\,d^2+15\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right )}{3}+5\,a^9\,c^9\,x^2\,\left (a\,d+b\,c\right )+\frac {b^9\,d^9\,x^{20}\,\left (a\,d+b\,c\right )}{2}+\frac {5\,a^8\,c^8\,x^3\,\left (9\,a^2\,d^2+20\,a\,b\,c\,d+9\,b^2\,c^2\right )}{3}+\frac {5\,b^8\,d^8\,x^{19}\,\left (9\,a^2\,d^2+20\,a\,b\,c\,d+9\,b^2\,c^2\right )}{19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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