Optimal. Leaf size=273 \[ -\frac {(b c-a d)^{10}}{19 b^{11} (a+b x)^{19}}-\frac {5 d (b c-a d)^9}{9 b^{11} (a+b x)^{18}}-\frac {45 d^2 (b c-a d)^8}{17 b^{11} (a+b x)^{17}}-\frac {15 d^3 (b c-a d)^7}{2 b^{11} (a+b x)^{16}}-\frac {14 d^4 (b c-a d)^6}{b^{11} (a+b x)^{15}}-\frac {18 d^5 (b c-a d)^5}{b^{11} (a+b x)^{14}}-\frac {210 d^6 (b c-a d)^4}{13 b^{11} (a+b x)^{13}}-\frac {10 d^7 (b c-a d)^3}{b^{11} (a+b x)^{12}}-\frac {45 d^8 (b c-a d)^2}{11 b^{11} (a+b x)^{11}}-\frac {d^9 (b c-a d)}{b^{11} (a+b x)^{10}}-\frac {d^{10}}{9 b^{11} (a+b x)^9} \]
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Rubi [A]
time = 0.21, antiderivative size = 273, 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 (b c-a d)}{b^{11} (a+b x)^{10}}-\frac {45 d^8 (b c-a d)^2}{11 b^{11} (a+b x)^{11}}-\frac {10 d^7 (b c-a d)^3}{b^{11} (a+b x)^{12}}-\frac {210 d^6 (b c-a d)^4}{13 b^{11} (a+b x)^{13}}-\frac {18 d^5 (b c-a d)^5}{b^{11} (a+b x)^{14}}-\frac {14 d^4 (b c-a d)^6}{b^{11} (a+b x)^{15}}-\frac {15 d^3 (b c-a d)^7}{2 b^{11} (a+b x)^{16}}-\frac {45 d^2 (b c-a d)^8}{17 b^{11} (a+b x)^{17}}-\frac {5 d (b c-a d)^9}{9 b^{11} (a+b x)^{18}}-\frac {(b c-a d)^{10}}{19 b^{11} (a+b x)^{19}}-\frac {d^{10}}{9 b^{11} (a+b x)^9} \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)^{20}} \, dx &=\int \left (\frac {(b c-a d)^{10}}{b^{10} (a+b x)^{20}}+\frac {10 d (b c-a d)^9}{b^{10} (a+b x)^{19}}+\frac {45 d^2 (b c-a d)^8}{b^{10} (a+b x)^{18}}+\frac {120 d^3 (b c-a d)^7}{b^{10} (a+b x)^{17}}+\frac {210 d^4 (b c-a d)^6}{b^{10} (a+b x)^{16}}+\frac {252 d^5 (b c-a d)^5}{b^{10} (a+b x)^{15}}+\frac {210 d^6 (b c-a d)^4}{b^{10} (a+b x)^{14}}+\frac {120 d^7 (b c-a d)^3}{b^{10} (a+b x)^{13}}+\frac {45 d^8 (b c-a d)^2}{b^{10} (a+b x)^{12}}+\frac {10 d^9 (b c-a d)}{b^{10} (a+b x)^{11}}+\frac {d^{10}}{b^{10} (a+b x)^{10}}\right ) \, dx\\ &=-\frac {(b c-a d)^{10}}{19 b^{11} (a+b x)^{19}}-\frac {5 d (b c-a d)^9}{9 b^{11} (a+b x)^{18}}-\frac {45 d^2 (b c-a d)^8}{17 b^{11} (a+b x)^{17}}-\frac {15 d^3 (b c-a d)^7}{2 b^{11} (a+b x)^{16}}-\frac {14 d^4 (b c-a d)^6}{b^{11} (a+b x)^{15}}-\frac {18 d^5 (b c-a d)^5}{b^{11} (a+b x)^{14}}-\frac {210 d^6 (b c-a d)^4}{13 b^{11} (a+b x)^{13}}-\frac {10 d^7 (b c-a d)^3}{b^{11} (a+b x)^{12}}-\frac {45 d^8 (b c-a d)^2}{11 b^{11} (a+b x)^{11}}-\frac {d^9 (b c-a d)}{b^{11} (a+b x)^{10}}-\frac {d^{10}}{9 b^{11} (a+b x)^9}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(692\) vs. \(2(273)=546\).
time = 0.19, size = 692, normalized size = 2.53 \begin {gather*} -\frac {a^{10} d^{10}+a^9 b d^9 (9 c+19 d x)+9 a^8 b^2 d^8 \left (5 c^2+19 c d x+19 d^2 x^2\right )+3 a^7 b^3 d^7 \left (55 c^3+285 c^2 d x+513 c d^2 x^2+323 d^3 x^3\right )+3 a^6 b^4 d^6 \left (165 c^4+1045 c^3 d x+2565 c^2 d^2 x^2+2907 c d^3 x^3+1292 d^4 x^4\right )+9 a^5 b^5 d^5 \left (143 c^5+1045 c^4 d x+3135 c^3 d^2 x^2+4845 c^2 d^3 x^3+3876 c d^4 x^4+1292 d^5 x^5\right )+3 a^4 b^6 d^4 \left (1001 c^6+8151 c^5 d x+28215 c^4 d^2 x^2+53295 c^3 d^3 x^3+58140 c^2 d^4 x^4+34884 c d^5 x^5+9044 d^6 x^6\right )+3 a^3 b^7 d^3 \left (2145 c^7+19019 c^6 d x+73359 c^5 d^2 x^2+159885 c^4 d^3 x^3+213180 c^3 d^4 x^4+174420 c^2 d^5 x^5+81396 c d^6 x^6+16796 d^7 x^7\right )+9 a^2 b^8 d^2 \left (1430 c^8+13585 c^7 d x+57057 c^6 d^2 x^2+138567 c^5 d^3 x^3+213180 c^4 d^4 x^4+213180 c^3 d^5 x^5+135660 c^2 d^6 x^6+50388 c d^7 x^7+8398 d^8 x^8\right )+a b^9 d \left (24310 c^9+244530 c^8 d x+1100385 c^7 d^2 x^2+2909907 c^6 d^3 x^3+4988412 c^5 d^4 x^4+5755860 c^4 d^5 x^5+4476780 c^3 d^6 x^6+2267460 c^2 d^7 x^7+680238 c d^8 x^8+92378 d^9 x^9\right )+b^{10} \left (43758 c^{10}+461890 c^9 d x+2200770 c^8 d^2 x^2+6235515 c^7 d^3 x^3+11639628 c^6 d^4 x^4+14965236 c^5 d^5 x^5+13430340 c^4 d^6 x^6+8314020 c^3 d^7 x^7+3401190 c^2 d^8 x^8+831402 c d^9 x^9+92378 d^{10} x^{10}\right )}{831402 b^{11} (a+b x)^{19}} \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. \(865\) vs.
\(2(259)=518\).
time = 0.15, size = 866, normalized size = 3.17 Too large to display
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. 1063 vs.
\(2 (259) = 518\).
time = 0.47, size = 1063, normalized size = 3.89 \begin {gather*} -\frac {92378 \, b^{10} d^{10} x^{10} + 43758 \, b^{10} c^{10} + 24310 \, a b^{9} c^{9} d + 12870 \, a^{2} b^{8} c^{8} d^{2} + 6435 \, a^{3} b^{7} c^{7} d^{3} + 3003 \, a^{4} b^{6} c^{6} d^{4} + 1287 \, a^{5} b^{5} c^{5} d^{5} + 495 \, a^{6} b^{4} c^{4} d^{6} + 165 \, a^{7} b^{3} c^{3} d^{7} + 45 \, a^{8} b^{2} c^{2} d^{8} + 9 \, a^{9} b c d^{9} + a^{10} d^{10} + 92378 \, {\left (9 \, b^{10} c d^{9} + a b^{9} d^{10}\right )} x^{9} + 75582 \, {\left (45 \, b^{10} c^{2} d^{8} + 9 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 50388 \, {\left (165 \, b^{10} c^{3} d^{7} + 45 \, a b^{9} c^{2} d^{8} + 9 \, a^{2} b^{8} c d^{9} + a^{3} b^{7} d^{10}\right )} x^{7} + 27132 \, {\left (495 \, b^{10} c^{4} d^{6} + 165 \, a b^{9} c^{3} d^{7} + 45 \, a^{2} b^{8} c^{2} d^{8} + 9 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 11628 \, {\left (1287 \, b^{10} c^{5} d^{5} + 495 \, a b^{9} c^{4} d^{6} + 165 \, a^{2} b^{8} c^{3} d^{7} + 45 \, a^{3} b^{7} c^{2} d^{8} + 9 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right )} x^{5} + 3876 \, {\left (3003 \, b^{10} c^{6} d^{4} + 1287 \, a b^{9} c^{5} d^{5} + 495 \, a^{2} b^{8} c^{4} d^{6} + 165 \, a^{3} b^{7} c^{3} d^{7} + 45 \, a^{4} b^{6} c^{2} d^{8} + 9 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 969 \, {\left (6435 \, b^{10} c^{7} d^{3} + 3003 \, a b^{9} c^{6} d^{4} + 1287 \, a^{2} b^{8} c^{5} d^{5} + 495 \, a^{3} b^{7} c^{4} d^{6} + 165 \, a^{4} b^{6} c^{3} d^{7} + 45 \, a^{5} b^{5} c^{2} d^{8} + 9 \, a^{6} b^{4} c d^{9} + a^{7} b^{3} d^{10}\right )} x^{3} + 171 \, {\left (12870 \, b^{10} c^{8} d^{2} + 6435 \, a b^{9} c^{7} d^{3} + 3003 \, a^{2} b^{8} c^{6} d^{4} + 1287 \, a^{3} b^{7} c^{5} d^{5} + 495 \, a^{4} b^{6} c^{4} d^{6} + 165 \, a^{5} b^{5} c^{3} d^{7} + 45 \, a^{6} b^{4} c^{2} d^{8} + 9 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 19 \, {\left (24310 \, b^{10} c^{9} d + 12870 \, a b^{9} c^{8} d^{2} + 6435 \, a^{2} b^{8} c^{7} d^{3} + 3003 \, a^{3} b^{7} c^{6} d^{4} + 1287 \, a^{4} b^{6} c^{5} d^{5} + 495 \, a^{5} b^{5} c^{4} d^{6} + 165 \, a^{6} b^{4} c^{3} d^{7} + 45 \, a^{7} b^{3} c^{2} d^{8} + 9 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x}{831402 \, {\left (b^{30} x^{19} + 19 \, a b^{29} x^{18} + 171 \, a^{2} b^{28} x^{17} + 969 \, a^{3} b^{27} x^{16} + 3876 \, a^{4} b^{26} x^{15} + 11628 \, a^{5} b^{25} x^{14} + 27132 \, a^{6} b^{24} x^{13} + 50388 \, a^{7} b^{23} x^{12} + 75582 \, a^{8} b^{22} x^{11} + 92378 \, a^{9} b^{21} x^{10} + 92378 \, a^{10} b^{20} x^{9} + 75582 \, a^{11} b^{19} x^{8} + 50388 \, a^{12} b^{18} x^{7} + 27132 \, a^{13} b^{17} x^{6} + 11628 \, a^{14} b^{16} x^{5} + 3876 \, a^{15} b^{15} x^{4} + 969 \, a^{16} b^{14} x^{3} + 171 \, a^{17} b^{13} x^{2} + 19 \, a^{18} b^{12} x + a^{19} b^{11}\right )}} \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. 1063 vs.
\(2 (259) = 518\).
time = 0.56, size = 1063, normalized size = 3.89 \begin {gather*} -\frac {92378 \, b^{10} d^{10} x^{10} + 43758 \, b^{10} c^{10} + 24310 \, a b^{9} c^{9} d + 12870 \, a^{2} b^{8} c^{8} d^{2} + 6435 \, a^{3} b^{7} c^{7} d^{3} + 3003 \, a^{4} b^{6} c^{6} d^{4} + 1287 \, a^{5} b^{5} c^{5} d^{5} + 495 \, a^{6} b^{4} c^{4} d^{6} + 165 \, a^{7} b^{3} c^{3} d^{7} + 45 \, a^{8} b^{2} c^{2} d^{8} + 9 \, a^{9} b c d^{9} + a^{10} d^{10} + 92378 \, {\left (9 \, b^{10} c d^{9} + a b^{9} d^{10}\right )} x^{9} + 75582 \, {\left (45 \, b^{10} c^{2} d^{8} + 9 \, a b^{9} c d^{9} + a^{2} b^{8} d^{10}\right )} x^{8} + 50388 \, {\left (165 \, b^{10} c^{3} d^{7} + 45 \, a b^{9} c^{2} d^{8} + 9 \, a^{2} b^{8} c d^{9} + a^{3} b^{7} d^{10}\right )} x^{7} + 27132 \, {\left (495 \, b^{10} c^{4} d^{6} + 165 \, a b^{9} c^{3} d^{7} + 45 \, a^{2} b^{8} c^{2} d^{8} + 9 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{6} + 11628 \, {\left (1287 \, b^{10} c^{5} d^{5} + 495 \, a b^{9} c^{4} d^{6} + 165 \, a^{2} b^{8} c^{3} d^{7} + 45 \, a^{3} b^{7} c^{2} d^{8} + 9 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right )} x^{5} + 3876 \, {\left (3003 \, b^{10} c^{6} d^{4} + 1287 \, a b^{9} c^{5} d^{5} + 495 \, a^{2} b^{8} c^{4} d^{6} + 165 \, a^{3} b^{7} c^{3} d^{7} + 45 \, a^{4} b^{6} c^{2} d^{8} + 9 \, a^{5} b^{5} c d^{9} + a^{6} b^{4} d^{10}\right )} x^{4} + 969 \, {\left (6435 \, b^{10} c^{7} d^{3} + 3003 \, a b^{9} c^{6} d^{4} + 1287 \, a^{2} b^{8} c^{5} d^{5} + 495 \, a^{3} b^{7} c^{4} d^{6} + 165 \, a^{4} b^{6} c^{3} d^{7} + 45 \, a^{5} b^{5} c^{2} d^{8} + 9 \, a^{6} b^{4} c d^{9} + a^{7} b^{3} d^{10}\right )} x^{3} + 171 \, {\left (12870 \, b^{10} c^{8} d^{2} + 6435 \, a b^{9} c^{7} d^{3} + 3003 \, a^{2} b^{8} c^{6} d^{4} + 1287 \, a^{3} b^{7} c^{5} d^{5} + 495 \, a^{4} b^{6} c^{4} d^{6} + 165 \, a^{5} b^{5} c^{3} d^{7} + 45 \, a^{6} b^{4} c^{2} d^{8} + 9 \, a^{7} b^{3} c d^{9} + a^{8} b^{2} d^{10}\right )} x^{2} + 19 \, {\left (24310 \, b^{10} c^{9} d + 12870 \, a b^{9} c^{8} d^{2} + 6435 \, a^{2} b^{8} c^{7} d^{3} + 3003 \, a^{3} b^{7} c^{6} d^{4} + 1287 \, a^{4} b^{6} c^{5} d^{5} + 495 \, a^{5} b^{5} c^{4} d^{6} + 165 \, a^{6} b^{4} c^{3} d^{7} + 45 \, a^{7} b^{3} c^{2} d^{8} + 9 \, a^{8} b^{2} c d^{9} + a^{9} b d^{10}\right )} x}{831402 \, {\left (b^{30} x^{19} + 19 \, a b^{29} x^{18} + 171 \, a^{2} b^{28} x^{17} + 969 \, a^{3} b^{27} x^{16} + 3876 \, a^{4} b^{26} x^{15} + 11628 \, a^{5} b^{25} x^{14} + 27132 \, a^{6} b^{24} x^{13} + 50388 \, a^{7} b^{23} x^{12} + 75582 \, a^{8} b^{22} x^{11} + 92378 \, a^{9} b^{21} x^{10} + 92378 \, a^{10} b^{20} x^{9} + 75582 \, a^{11} b^{19} x^{8} + 50388 \, a^{12} b^{18} x^{7} + 27132 \, a^{13} b^{17} x^{6} + 11628 \, a^{14} b^{16} x^{5} + 3876 \, a^{15} b^{15} x^{4} + 969 \, a^{16} b^{14} x^{3} + 171 \, a^{17} b^{13} x^{2} + 19 \, a^{18} b^{12} x + a^{19} b^{11}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 961 vs.
\(2 (259) = 518\).
time = 0.80, size = 961, normalized size = 3.52 \begin {gather*} -\frac {92378 \, b^{10} d^{10} x^{10} + 831402 \, b^{10} c d^{9} x^{9} + 92378 \, a b^{9} d^{10} x^{9} + 3401190 \, b^{10} c^{2} d^{8} x^{8} + 680238 \, a b^{9} c d^{9} x^{8} + 75582 \, a^{2} b^{8} d^{10} x^{8} + 8314020 \, b^{10} c^{3} d^{7} x^{7} + 2267460 \, a b^{9} c^{2} d^{8} x^{7} + 453492 \, a^{2} b^{8} c d^{9} x^{7} + 50388 \, a^{3} b^{7} d^{10} x^{7} + 13430340 \, b^{10} c^{4} d^{6} x^{6} + 4476780 \, a b^{9} c^{3} d^{7} x^{6} + 1220940 \, a^{2} b^{8} c^{2} d^{8} x^{6} + 244188 \, a^{3} b^{7} c d^{9} x^{6} + 27132 \, a^{4} b^{6} d^{10} x^{6} + 14965236 \, b^{10} c^{5} d^{5} x^{5} + 5755860 \, a b^{9} c^{4} d^{6} x^{5} + 1918620 \, a^{2} b^{8} c^{3} d^{7} x^{5} + 523260 \, a^{3} b^{7} c^{2} d^{8} x^{5} + 104652 \, a^{4} b^{6} c d^{9} x^{5} + 11628 \, a^{5} b^{5} d^{10} x^{5} + 11639628 \, b^{10} c^{6} d^{4} x^{4} + 4988412 \, a b^{9} c^{5} d^{5} x^{4} + 1918620 \, a^{2} b^{8} c^{4} d^{6} x^{4} + 639540 \, a^{3} b^{7} c^{3} d^{7} x^{4} + 174420 \, a^{4} b^{6} c^{2} d^{8} x^{4} + 34884 \, a^{5} b^{5} c d^{9} x^{4} + 3876 \, a^{6} b^{4} d^{10} x^{4} + 6235515 \, b^{10} c^{7} d^{3} x^{3} + 2909907 \, a b^{9} c^{6} d^{4} x^{3} + 1247103 \, a^{2} b^{8} c^{5} d^{5} x^{3} + 479655 \, a^{3} b^{7} c^{4} d^{6} x^{3} + 159885 \, a^{4} b^{6} c^{3} d^{7} x^{3} + 43605 \, a^{5} b^{5} c^{2} d^{8} x^{3} + 8721 \, a^{6} b^{4} c d^{9} x^{3} + 969 \, a^{7} b^{3} d^{10} x^{3} + 2200770 \, b^{10} c^{8} d^{2} x^{2} + 1100385 \, a b^{9} c^{7} d^{3} x^{2} + 513513 \, a^{2} b^{8} c^{6} d^{4} x^{2} + 220077 \, a^{3} b^{7} c^{5} d^{5} x^{2} + 84645 \, a^{4} b^{6} c^{4} d^{6} x^{2} + 28215 \, a^{5} b^{5} c^{3} d^{7} x^{2} + 7695 \, a^{6} b^{4} c^{2} d^{8} x^{2} + 1539 \, a^{7} b^{3} c d^{9} x^{2} + 171 \, a^{8} b^{2} d^{10} x^{2} + 461890 \, b^{10} c^{9} d x + 244530 \, a b^{9} c^{8} d^{2} x + 122265 \, a^{2} b^{8} c^{7} d^{3} x + 57057 \, a^{3} b^{7} c^{6} d^{4} x + 24453 \, a^{4} b^{6} c^{5} d^{5} x + 9405 \, a^{5} b^{5} c^{4} d^{6} x + 3135 \, a^{6} b^{4} c^{3} d^{7} x + 855 \, a^{7} b^{3} c^{2} d^{8} x + 171 \, a^{8} b^{2} c d^{9} x + 19 \, a^{9} b d^{10} x + 43758 \, b^{10} c^{10} + 24310 \, a b^{9} c^{9} d + 12870 \, a^{2} b^{8} c^{8} d^{2} + 6435 \, a^{3} b^{7} c^{7} d^{3} + 3003 \, a^{4} b^{6} c^{6} d^{4} + 1287 \, a^{5} b^{5} c^{5} d^{5} + 495 \, a^{6} b^{4} c^{4} d^{6} + 165 \, a^{7} b^{3} c^{3} d^{7} + 45 \, a^{8} b^{2} c^{2} d^{8} + 9 \, a^{9} b c d^{9} + a^{10} d^{10}}{831402 \, {\left (b x + a\right )}^{19} b^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 25.72, size = 1164, normalized size = 4.26 \begin {gather*} -\frac {a^{10}\,d^{10}+9\,a^9\,b\,c\,d^9+19\,a^9\,b\,d^{10}\,x+45\,a^8\,b^2\,c^2\,d^8+171\,a^8\,b^2\,c\,d^9\,x+171\,a^8\,b^2\,d^{10}\,x^2+165\,a^7\,b^3\,c^3\,d^7+855\,a^7\,b^3\,c^2\,d^8\,x+1539\,a^7\,b^3\,c\,d^9\,x^2+969\,a^7\,b^3\,d^{10}\,x^3+495\,a^6\,b^4\,c^4\,d^6+3135\,a^6\,b^4\,c^3\,d^7\,x+7695\,a^6\,b^4\,c^2\,d^8\,x^2+8721\,a^6\,b^4\,c\,d^9\,x^3+3876\,a^6\,b^4\,d^{10}\,x^4+1287\,a^5\,b^5\,c^5\,d^5+9405\,a^5\,b^5\,c^4\,d^6\,x+28215\,a^5\,b^5\,c^3\,d^7\,x^2+43605\,a^5\,b^5\,c^2\,d^8\,x^3+34884\,a^5\,b^5\,c\,d^9\,x^4+11628\,a^5\,b^5\,d^{10}\,x^5+3003\,a^4\,b^6\,c^6\,d^4+24453\,a^4\,b^6\,c^5\,d^5\,x+84645\,a^4\,b^6\,c^4\,d^6\,x^2+159885\,a^4\,b^6\,c^3\,d^7\,x^3+174420\,a^4\,b^6\,c^2\,d^8\,x^4+104652\,a^4\,b^6\,c\,d^9\,x^5+27132\,a^4\,b^6\,d^{10}\,x^6+6435\,a^3\,b^7\,c^7\,d^3+57057\,a^3\,b^7\,c^6\,d^4\,x+220077\,a^3\,b^7\,c^5\,d^5\,x^2+479655\,a^3\,b^7\,c^4\,d^6\,x^3+639540\,a^3\,b^7\,c^3\,d^7\,x^4+523260\,a^3\,b^7\,c^2\,d^8\,x^5+244188\,a^3\,b^7\,c\,d^9\,x^6+50388\,a^3\,b^7\,d^{10}\,x^7+12870\,a^2\,b^8\,c^8\,d^2+122265\,a^2\,b^8\,c^7\,d^3\,x+513513\,a^2\,b^8\,c^6\,d^4\,x^2+1247103\,a^2\,b^8\,c^5\,d^5\,x^3+1918620\,a^2\,b^8\,c^4\,d^6\,x^4+1918620\,a^2\,b^8\,c^3\,d^7\,x^5+1220940\,a^2\,b^8\,c^2\,d^8\,x^6+453492\,a^2\,b^8\,c\,d^9\,x^7+75582\,a^2\,b^8\,d^{10}\,x^8+24310\,a\,b^9\,c^9\,d+244530\,a\,b^9\,c^8\,d^2\,x+1100385\,a\,b^9\,c^7\,d^3\,x^2+2909907\,a\,b^9\,c^6\,d^4\,x^3+4988412\,a\,b^9\,c^5\,d^5\,x^4+5755860\,a\,b^9\,c^4\,d^6\,x^5+4476780\,a\,b^9\,c^3\,d^7\,x^6+2267460\,a\,b^9\,c^2\,d^8\,x^7+680238\,a\,b^9\,c\,d^9\,x^8+92378\,a\,b^9\,d^{10}\,x^9+43758\,b^{10}\,c^{10}+461890\,b^{10}\,c^9\,d\,x+2200770\,b^{10}\,c^8\,d^2\,x^2+6235515\,b^{10}\,c^7\,d^3\,x^3+11639628\,b^{10}\,c^6\,d^4\,x^4+14965236\,b^{10}\,c^5\,d^5\,x^5+13430340\,b^{10}\,c^4\,d^6\,x^6+8314020\,b^{10}\,c^3\,d^7\,x^7+3401190\,b^{10}\,c^2\,d^8\,x^8+831402\,b^{10}\,c\,d^9\,x^9+92378\,b^{10}\,d^{10}\,x^{10}}{831402\,a^{19}\,b^{11}+15796638\,a^{18}\,b^{12}\,x+142169742\,a^{17}\,b^{13}\,x^2+805628538\,a^{16}\,b^{14}\,x^3+3222514152\,a^{15}\,b^{15}\,x^4+9667542456\,a^{14}\,b^{16}\,x^5+22557599064\,a^{13}\,b^{17}\,x^6+41892683976\,a^{12}\,b^{18}\,x^7+62839025964\,a^{11}\,b^{19}\,x^8+76803253956\,a^{10}\,b^{20}\,x^9+76803253956\,a^9\,b^{21}\,x^{10}+62839025964\,a^8\,b^{22}\,x^{11}+41892683976\,a^7\,b^{23}\,x^{12}+22557599064\,a^6\,b^{24}\,x^{13}+9667542456\,a^5\,b^{25}\,x^{14}+3222514152\,a^4\,b^{26}\,x^{15}+805628538\,a^3\,b^{27}\,x^{16}+142169742\,a^2\,b^{28}\,x^{17}+15796638\,a\,b^{29}\,x^{18}+831402\,b^{30}\,x^{19}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
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