Optimal. Leaf size=200 \[ \frac {7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac {7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac {5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac {35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac {7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac {7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac {(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac {d^7 (a+b x)^{17}}{17 b^8} \]
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Rubi [A] time = 0.68, antiderivative size = 200, 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 = {43} \begin {gather*} \frac {7 d^6 (a+b x)^{16} (b c-a d)}{16 b^8}+\frac {7 d^5 (a+b x)^{15} (b c-a d)^2}{5 b^8}+\frac {5 d^4 (a+b x)^{14} (b c-a d)^3}{2 b^8}+\frac {35 d^3 (a+b x)^{13} (b c-a d)^4}{13 b^8}+\frac {7 d^2 (a+b x)^{12} (b c-a d)^5}{4 b^8}+\frac {7 d (a+b x)^{11} (b c-a d)^6}{11 b^8}+\frac {(a+b x)^{10} (b c-a d)^7}{10 b^8}+\frac {d^7 (a+b x)^{17}}{17 b^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int (a+b x)^9 (c+d x)^7 \, dx &=\int \left (\frac {(b c-a d)^7 (a+b x)^9}{b^7}+\frac {7 d (b c-a d)^6 (a+b x)^{10}}{b^7}+\frac {21 d^2 (b c-a d)^5 (a+b x)^{11}}{b^7}+\frac {35 d^3 (b c-a d)^4 (a+b x)^{12}}{b^7}+\frac {35 d^4 (b c-a d)^3 (a+b x)^{13}}{b^7}+\frac {21 d^5 (b c-a d)^2 (a+b x)^{14}}{b^7}+\frac {7 d^6 (b c-a d) (a+b x)^{15}}{b^7}+\frac {d^7 (a+b x)^{16}}{b^7}\right ) \, dx\\ &=\frac {(b c-a d)^7 (a+b x)^{10}}{10 b^8}+\frac {7 d (b c-a d)^6 (a+b x)^{11}}{11 b^8}+\frac {7 d^2 (b c-a d)^5 (a+b x)^{12}}{4 b^8}+\frac {35 d^3 (b c-a d)^4 (a+b x)^{13}}{13 b^8}+\frac {5 d^4 (b c-a d)^3 (a+b x)^{14}}{2 b^8}+\frac {7 d^5 (b c-a d)^2 (a+b x)^{15}}{5 b^8}+\frac {7 d^6 (b c-a d) (a+b x)^{16}}{16 b^8}+\frac {d^7 (a+b x)^{17}}{17 b^8}\\ \end {align*}
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Mathematica [B] time = 0.15, size = 993, normalized size = 4.96 \begin {gather*} \frac {1}{17} b^9 d^7 x^{17}+\frac {1}{16} b^8 d^6 (7 b c+9 a d) x^{16}+\frac {1}{5} b^7 d^5 \left (7 b^2 c^2+21 a b d c+12 a^2 d^2\right ) x^{15}+\frac {1}{2} b^6 d^4 \left (5 b^3 c^3+27 a b^2 d c^2+36 a^2 b d^2 c+12 a^3 d^3\right ) x^{14}+\frac {7}{13} b^5 d^3 \left (5 b^4 c^4+45 a b^3 d c^3+108 a^2 b^2 d^2 c^2+84 a^3 b d^3 c+18 a^4 d^4\right ) x^{13}+\frac {7}{4} b^4 d^2 \left (b^5 c^5+15 a b^4 d c^4+60 a^2 b^3 d^2 c^3+84 a^3 b^2 d^3 c^2+42 a^4 b d^4 c+6 a^5 d^5\right ) x^{12}+\frac {7}{11} b^3 d \left (b^6 c^6+27 a b^5 d c^5+180 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+378 a^4 b^2 d^4 c^2+126 a^5 b d^5 c+12 a^6 d^6\right ) x^{11}+\frac {1}{10} b^2 \left (b^7 c^7+63 a b^6 d c^6+756 a^2 b^5 d^2 c^5+2940 a^3 b^4 d^3 c^4+4410 a^4 b^3 d^4 c^3+2646 a^5 b^2 d^5 c^2+588 a^6 b d^6 c+36 a^7 d^7\right ) x^{10}+a b \left (b^7 c^7+28 a b^6 d c^6+196 a^2 b^5 d^2 c^5+490 a^3 b^4 d^3 c^4+490 a^4 b^3 d^4 c^3+196 a^5 b^2 d^5 c^2+28 a^6 b d^6 c+a^7 d^7\right ) x^9+\frac {1}{8} a^2 \left (36 b^7 c^7+588 a b^6 d c^6+2646 a^2 b^5 d^2 c^5+4410 a^3 b^4 d^3 c^4+2940 a^4 b^3 d^4 c^3+756 a^5 b^2 d^5 c^2+63 a^6 b d^6 c+a^7 d^7\right ) x^8+a^3 c \left (12 b^6 c^6+126 a b^5 d c^5+378 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+180 a^4 b^2 d^4 c^2+27 a^5 b d^5 c+a^6 d^6\right ) x^7+\frac {7}{2} a^4 c^2 \left (6 b^5 c^5+42 a b^4 d c^4+84 a^2 b^3 d^2 c^3+60 a^3 b^2 d^3 c^2+15 a^4 b d^4 c+a^5 d^5\right ) x^6+\frac {7}{5} a^5 c^3 \left (18 b^4 c^4+84 a b^3 d c^3+108 a^2 b^2 d^2 c^2+45 a^3 b d^3 c+5 a^4 d^4\right ) x^5+\frac {7}{4} a^6 c^4 \left (12 b^3 c^3+36 a b^2 d c^2+27 a^2 b d^2 c+5 a^3 d^3\right ) x^4+a^7 c^5 \left (12 b^2 c^2+21 a b d c+7 a^2 d^2\right ) x^3+\frac {1}{2} a^8 c^6 (9 b c+7 a d) x^2+a^9 c^7 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (a+b x)^9 (c+d x)^7 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 0.86, size = 1175, normalized size = 5.88 \begin {gather*} \frac {1}{17} x^{17} d^{7} b^{9} + \frac {7}{16} x^{16} d^{6} c b^{9} + \frac {9}{16} x^{16} d^{7} b^{8} a + \frac {7}{5} x^{15} d^{5} c^{2} b^{9} + \frac {21}{5} x^{15} d^{6} c b^{8} a + \frac {12}{5} x^{15} d^{7} b^{7} a^{2} + \frac {5}{2} x^{14} d^{4} c^{3} b^{9} + \frac {27}{2} x^{14} d^{5} c^{2} b^{8} a + 18 x^{14} d^{6} c b^{7} a^{2} + 6 x^{14} d^{7} b^{6} a^{3} + \frac {35}{13} x^{13} d^{3} c^{4} b^{9} + \frac {315}{13} x^{13} d^{4} c^{3} b^{8} a + \frac {756}{13} x^{13} d^{5} c^{2} b^{7} a^{2} + \frac {588}{13} x^{13} d^{6} c b^{6} a^{3} + \frac {126}{13} x^{13} d^{7} b^{5} a^{4} + \frac {7}{4} x^{12} d^{2} c^{5} b^{9} + \frac {105}{4} x^{12} d^{3} c^{4} b^{8} a + 105 x^{12} d^{4} c^{3} b^{7} a^{2} + 147 x^{12} d^{5} c^{2} b^{6} a^{3} + \frac {147}{2} x^{12} d^{6} c b^{5} a^{4} + \frac {21}{2} x^{12} d^{7} b^{4} a^{5} + \frac {7}{11} x^{11} d c^{6} b^{9} + \frac {189}{11} x^{11} d^{2} c^{5} b^{8} a + \frac {1260}{11} x^{11} d^{3} c^{4} b^{7} a^{2} + \frac {2940}{11} x^{11} d^{4} c^{3} b^{6} a^{3} + \frac {2646}{11} x^{11} d^{5} c^{2} b^{5} a^{4} + \frac {882}{11} x^{11} d^{6} c b^{4} a^{5} + \frac {84}{11} x^{11} d^{7} b^{3} a^{6} + \frac {1}{10} x^{10} c^{7} b^{9} + \frac {63}{10} x^{10} d c^{6} b^{8} a + \frac {378}{5} x^{10} d^{2} c^{5} b^{7} a^{2} + 294 x^{10} d^{3} c^{4} b^{6} a^{3} + 441 x^{10} d^{4} c^{3} b^{5} a^{4} + \frac {1323}{5} x^{10} d^{5} c^{2} b^{4} a^{5} + \frac {294}{5} x^{10} d^{6} c b^{3} a^{6} + \frac {18}{5} x^{10} d^{7} b^{2} a^{7} + x^{9} c^{7} b^{8} a + 28 x^{9} d c^{6} b^{7} a^{2} + 196 x^{9} d^{2} c^{5} b^{6} a^{3} + 490 x^{9} d^{3} c^{4} b^{5} a^{4} + 490 x^{9} d^{4} c^{3} b^{4} a^{5} + 196 x^{9} d^{5} c^{2} b^{3} a^{6} + 28 x^{9} d^{6} c b^{2} a^{7} + x^{9} d^{7} b a^{8} + \frac {9}{2} x^{8} c^{7} b^{7} a^{2} + \frac {147}{2} x^{8} d c^{6} b^{6} a^{3} + \frac {1323}{4} x^{8} d^{2} c^{5} b^{5} a^{4} + \frac {2205}{4} x^{8} d^{3} c^{4} b^{4} a^{5} + \frac {735}{2} x^{8} d^{4} c^{3} b^{3} a^{6} + \frac {189}{2} x^{8} d^{5} c^{2} b^{2} a^{7} + \frac {63}{8} x^{8} d^{6} c b a^{8} + \frac {1}{8} x^{8} d^{7} a^{9} + 12 x^{7} c^{7} b^{6} a^{3} + 126 x^{7} d c^{6} b^{5} a^{4} + 378 x^{7} d^{2} c^{5} b^{4} a^{5} + 420 x^{7} d^{3} c^{4} b^{3} a^{6} + 180 x^{7} d^{4} c^{3} b^{2} a^{7} + 27 x^{7} d^{5} c^{2} b a^{8} + x^{7} d^{6} c a^{9} + 21 x^{6} c^{7} b^{5} a^{4} + 147 x^{6} d c^{6} b^{4} a^{5} + 294 x^{6} d^{2} c^{5} b^{3} a^{6} + 210 x^{6} d^{3} c^{4} b^{2} a^{7} + \frac {105}{2} x^{6} d^{4} c^{3} b a^{8} + \frac {7}{2} x^{6} d^{5} c^{2} a^{9} + \frac {126}{5} x^{5} c^{7} b^{4} a^{5} + \frac {588}{5} x^{5} d c^{6} b^{3} a^{6} + \frac {756}{5} x^{5} d^{2} c^{5} b^{2} a^{7} + 63 x^{5} d^{3} c^{4} b a^{8} + 7 x^{5} d^{4} c^{3} a^{9} + 21 x^{4} c^{7} b^{3} a^{6} + 63 x^{4} d c^{6} b^{2} a^{7} + \frac {189}{4} x^{4} d^{2} c^{5} b a^{8} + \frac {35}{4} x^{4} d^{3} c^{4} a^{9} + 12 x^{3} c^{7} b^{2} a^{7} + 21 x^{3} d c^{6} b a^{8} + 7 x^{3} d^{2} c^{5} a^{9} + \frac {9}{2} x^{2} c^{7} b a^{8} + \frac {7}{2} x^{2} d c^{6} a^{9} + x c^{7} a^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.05, size = 1175, normalized size = 5.88
result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 1033, normalized size = 5.16 \begin {gather*} \frac {b^{9} d^{7} x^{17}}{17}+a^{9} c^{7} x +\frac {\left (9 a \,b^{8} d^{7}+7 b^{9} c \,d^{6}\right ) x^{16}}{16}+\frac {\left (36 a^{2} b^{7} d^{7}+63 a \,b^{8} c \,d^{6}+21 b^{9} c^{2} d^{5}\right ) x^{15}}{15}+\frac {\left (84 a^{3} b^{6} d^{7}+252 a^{2} b^{7} c \,d^{6}+189 a \,b^{8} c^{2} d^{5}+35 b^{9} c^{3} d^{4}\right ) x^{14}}{14}+\frac {\left (126 a^{4} b^{5} d^{7}+588 a^{3} b^{6} c \,d^{6}+756 a^{2} b^{7} c^{2} d^{5}+315 a \,b^{8} c^{3} d^{4}+35 b^{9} c^{4} d^{3}\right ) x^{13}}{13}+\frac {\left (126 a^{5} b^{4} d^{7}+882 a^{4} b^{5} c \,d^{6}+1764 a^{3} b^{6} c^{2} d^{5}+1260 a^{2} b^{7} c^{3} d^{4}+315 a \,b^{8} c^{4} d^{3}+21 b^{9} c^{5} d^{2}\right ) x^{12}}{12}+\frac {\left (84 a^{6} b^{3} d^{7}+882 a^{5} b^{4} c \,d^{6}+2646 a^{4} b^{5} c^{2} d^{5}+2940 a^{3} b^{6} c^{3} d^{4}+1260 a^{2} b^{7} c^{4} d^{3}+189 a \,b^{8} c^{5} d^{2}+7 b^{9} c^{6} d \right ) x^{11}}{11}+\frac {\left (36 a^{7} b^{2} d^{7}+588 a^{6} b^{3} c \,d^{6}+2646 a^{5} b^{4} c^{2} d^{5}+4410 a^{4} b^{5} c^{3} d^{4}+2940 a^{3} b^{6} c^{4} d^{3}+756 a^{2} b^{7} c^{5} d^{2}+63 a \,b^{8} c^{6} d +b^{9} c^{7}\right ) x^{10}}{10}+\frac {\left (9 a^{8} b \,d^{7}+252 a^{7} b^{2} c \,d^{6}+1764 a^{6} b^{3} c^{2} d^{5}+4410 a^{5} b^{4} c^{3} d^{4}+4410 a^{4} b^{5} c^{4} d^{3}+1764 a^{3} b^{6} c^{5} d^{2}+252 a^{2} b^{7} c^{6} d +9 a \,b^{8} c^{7}\right ) x^{9}}{9}+\frac {\left (a^{9} d^{7}+63 a^{8} b c \,d^{6}+756 a^{7} b^{2} c^{2} d^{5}+2940 a^{6} b^{3} c^{3} d^{4}+4410 a^{5} b^{4} c^{4} d^{3}+2646 a^{4} b^{5} c^{5} d^{2}+588 a^{3} b^{6} c^{6} d +36 a^{2} b^{7} c^{7}\right ) x^{8}}{8}+\frac {\left (7 a^{9} c \,d^{6}+189 a^{8} b \,c^{2} d^{5}+1260 a^{7} b^{2} c^{3} d^{4}+2940 a^{6} b^{3} c^{4} d^{3}+2646 a^{5} b^{4} c^{5} d^{2}+882 a^{4} b^{5} c^{6} d +84 a^{3} b^{6} c^{7}\right ) x^{7}}{7}+\frac {\left (21 a^{9} c^{2} d^{5}+315 a^{8} b \,c^{3} d^{4}+1260 a^{7} b^{2} c^{4} d^{3}+1764 a^{6} b^{3} c^{5} d^{2}+882 a^{5} b^{4} c^{6} d +126 a^{4} b^{5} c^{7}\right ) x^{6}}{6}+\frac {\left (35 a^{9} c^{3} d^{4}+315 a^{8} b \,c^{4} d^{3}+756 a^{7} b^{2} c^{5} d^{2}+588 a^{6} b^{3} c^{6} d +126 a^{5} b^{4} c^{7}\right ) x^{5}}{5}+\frac {\left (35 a^{9} c^{4} d^{3}+189 a^{8} b \,c^{5} d^{2}+252 a^{7} b^{2} c^{6} d +84 a^{6} b^{3} c^{7}\right ) x^{4}}{4}+\frac {\left (21 a^{9} c^{5} d^{2}+63 a^{8} b \,c^{6} d +36 a^{7} b^{2} c^{7}\right ) x^{3}}{3}+\frac {\left (7 a^{9} c^{6} d +9 a^{8} b \,c^{7}\right ) x^{2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.43, size = 1023, normalized size = 5.12 \begin {gather*} \frac {1}{17} \, b^{9} d^{7} x^{17} + a^{9} c^{7} x + \frac {1}{16} \, {\left (7 \, b^{9} c d^{6} + 9 \, a b^{8} d^{7}\right )} x^{16} + \frac {1}{5} \, {\left (7 \, b^{9} c^{2} d^{5} + 21 \, a b^{8} c d^{6} + 12 \, a^{2} b^{7} d^{7}\right )} x^{15} + \frac {1}{2} \, {\left (5 \, b^{9} c^{3} d^{4} + 27 \, a b^{8} c^{2} d^{5} + 36 \, a^{2} b^{7} c d^{6} + 12 \, a^{3} b^{6} d^{7}\right )} x^{14} + \frac {7}{13} \, {\left (5 \, b^{9} c^{4} d^{3} + 45 \, a b^{8} c^{3} d^{4} + 108 \, a^{2} b^{7} c^{2} d^{5} + 84 \, a^{3} b^{6} c d^{6} + 18 \, a^{4} b^{5} d^{7}\right )} x^{13} + \frac {7}{4} \, {\left (b^{9} c^{5} d^{2} + 15 \, a b^{8} c^{4} d^{3} + 60 \, a^{2} b^{7} c^{3} d^{4} + 84 \, a^{3} b^{6} c^{2} d^{5} + 42 \, a^{4} b^{5} c d^{6} + 6 \, a^{5} b^{4} d^{7}\right )} x^{12} + \frac {7}{11} \, {\left (b^{9} c^{6} d + 27 \, a b^{8} c^{5} d^{2} + 180 \, a^{2} b^{7} c^{4} d^{3} + 420 \, a^{3} b^{6} c^{3} d^{4} + 378 \, a^{4} b^{5} c^{2} d^{5} + 126 \, a^{5} b^{4} c d^{6} + 12 \, a^{6} b^{3} d^{7}\right )} x^{11} + \frac {1}{10} \, {\left (b^{9} c^{7} + 63 \, a b^{8} c^{6} d + 756 \, a^{2} b^{7} c^{5} d^{2} + 2940 \, a^{3} b^{6} c^{4} d^{3} + 4410 \, a^{4} b^{5} c^{3} d^{4} + 2646 \, a^{5} b^{4} c^{2} d^{5} + 588 \, a^{6} b^{3} c d^{6} + 36 \, a^{7} b^{2} d^{7}\right )} x^{10} + {\left (a b^{8} c^{7} + 28 \, a^{2} b^{7} c^{6} d + 196 \, a^{3} b^{6} c^{5} d^{2} + 490 \, a^{4} b^{5} c^{4} d^{3} + 490 \, a^{5} b^{4} c^{3} d^{4} + 196 \, a^{6} b^{3} c^{2} d^{5} + 28 \, a^{7} b^{2} c d^{6} + a^{8} b d^{7}\right )} x^{9} + \frac {1}{8} \, {\left (36 \, a^{2} b^{7} c^{7} + 588 \, a^{3} b^{6} c^{6} d + 2646 \, a^{4} b^{5} c^{5} d^{2} + 4410 \, a^{5} b^{4} c^{4} d^{3} + 2940 \, a^{6} b^{3} c^{3} d^{4} + 756 \, a^{7} b^{2} c^{2} d^{5} + 63 \, a^{8} b c d^{6} + a^{9} d^{7}\right )} x^{8} + {\left (12 \, a^{3} b^{6} c^{7} + 126 \, a^{4} b^{5} c^{6} d + 378 \, a^{5} b^{4} c^{5} d^{2} + 420 \, a^{6} b^{3} c^{4} d^{3} + 180 \, a^{7} b^{2} c^{3} d^{4} + 27 \, a^{8} b c^{2} d^{5} + a^{9} c d^{6}\right )} x^{7} + \frac {7}{2} \, {\left (6 \, a^{4} b^{5} c^{7} + 42 \, a^{5} b^{4} c^{6} d + 84 \, a^{6} b^{3} c^{5} d^{2} + 60 \, a^{7} b^{2} c^{4} d^{3} + 15 \, a^{8} b c^{3} d^{4} + a^{9} c^{2} d^{5}\right )} x^{6} + \frac {7}{5} \, {\left (18 \, a^{5} b^{4} c^{7} + 84 \, a^{6} b^{3} c^{6} d + 108 \, a^{7} b^{2} c^{5} d^{2} + 45 \, a^{8} b c^{4} d^{3} + 5 \, a^{9} c^{3} d^{4}\right )} x^{5} + \frac {7}{4} \, {\left (12 \, a^{6} b^{3} c^{7} + 36 \, a^{7} b^{2} c^{6} d + 27 \, a^{8} b c^{5} d^{2} + 5 \, a^{9} c^{4} d^{3}\right )} x^{4} + {\left (12 \, a^{7} b^{2} c^{7} + 21 \, a^{8} b c^{6} d + 7 \, a^{9} c^{5} d^{2}\right )} x^{3} + \frac {1}{2} \, {\left (9 \, a^{8} b c^{7} + 7 \, a^{9} c^{6} d\right )} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.55, size = 997, normalized size = 4.98 \begin {gather*} x^5\,\left (7\,a^9\,c^3\,d^4+63\,a^8\,b\,c^4\,d^3+\frac {756\,a^7\,b^2\,c^5\,d^2}{5}+\frac {588\,a^6\,b^3\,c^6\,d}{5}+\frac {126\,a^5\,b^4\,c^7}{5}\right )+x^{13}\,\left (\frac {126\,a^4\,b^5\,d^7}{13}+\frac {588\,a^3\,b^6\,c\,d^6}{13}+\frac {756\,a^2\,b^7\,c^2\,d^5}{13}+\frac {315\,a\,b^8\,c^3\,d^4}{13}+\frac {35\,b^9\,c^4\,d^3}{13}\right )+x^8\,\left (\frac {a^9\,d^7}{8}+\frac {63\,a^8\,b\,c\,d^6}{8}+\frac {189\,a^7\,b^2\,c^2\,d^5}{2}+\frac {735\,a^6\,b^3\,c^3\,d^4}{2}+\frac {2205\,a^5\,b^4\,c^4\,d^3}{4}+\frac {1323\,a^4\,b^5\,c^5\,d^2}{4}+\frac {147\,a^3\,b^6\,c^6\,d}{2}+\frac {9\,a^2\,b^7\,c^7}{2}\right )+x^{10}\,\left (\frac {18\,a^7\,b^2\,d^7}{5}+\frac {294\,a^6\,b^3\,c\,d^6}{5}+\frac {1323\,a^5\,b^4\,c^2\,d^5}{5}+441\,a^4\,b^5\,c^3\,d^4+294\,a^3\,b^6\,c^4\,d^3+\frac {378\,a^2\,b^7\,c^5\,d^2}{5}+\frac {63\,a\,b^8\,c^6\,d}{10}+\frac {b^9\,c^7}{10}\right )+x^6\,\left (\frac {7\,a^9\,c^2\,d^5}{2}+\frac {105\,a^8\,b\,c^3\,d^4}{2}+210\,a^7\,b^2\,c^4\,d^3+294\,a^6\,b^3\,c^5\,d^2+147\,a^5\,b^4\,c^6\,d+21\,a^4\,b^5\,c^7\right )+x^{12}\,\left (\frac {21\,a^5\,b^4\,d^7}{2}+\frac {147\,a^4\,b^5\,c\,d^6}{2}+147\,a^3\,b^6\,c^2\,d^5+105\,a^2\,b^7\,c^3\,d^4+\frac {105\,a\,b^8\,c^4\,d^3}{4}+\frac {7\,b^9\,c^5\,d^2}{4}\right )+x^7\,\left (a^9\,c\,d^6+27\,a^8\,b\,c^2\,d^5+180\,a^7\,b^2\,c^3\,d^4+420\,a^6\,b^3\,c^4\,d^3+378\,a^5\,b^4\,c^5\,d^2+126\,a^4\,b^5\,c^6\,d+12\,a^3\,b^6\,c^7\right )+x^{11}\,\left (\frac {84\,a^6\,b^3\,d^7}{11}+\frac {882\,a^5\,b^4\,c\,d^6}{11}+\frac {2646\,a^4\,b^5\,c^2\,d^5}{11}+\frac {2940\,a^3\,b^6\,c^3\,d^4}{11}+\frac {1260\,a^2\,b^7\,c^4\,d^3}{11}+\frac {189\,a\,b^8\,c^5\,d^2}{11}+\frac {7\,b^9\,c^6\,d}{11}\right )+x^9\,\left (a^8\,b\,d^7+28\,a^7\,b^2\,c\,d^6+196\,a^6\,b^3\,c^2\,d^5+490\,a^5\,b^4\,c^3\,d^4+490\,a^4\,b^5\,c^4\,d^3+196\,a^3\,b^6\,c^5\,d^2+28\,a^2\,b^7\,c^6\,d+a\,b^8\,c^7\right )+a^9\,c^7\,x+\frac {b^9\,d^7\,x^{17}}{17}+\frac {7\,a^6\,c^4\,x^4\,\left (5\,a^3\,d^3+27\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right )}{4}+\frac {b^6\,d^4\,x^{14}\,\left (12\,a^3\,d^3+36\,a^2\,b\,c\,d^2+27\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right )}{2}+\frac {a^8\,c^6\,x^2\,\left (7\,a\,d+9\,b\,c\right )}{2}+\frac {b^8\,d^6\,x^{16}\,\left (9\,a\,d+7\,b\,c\right )}{16}+a^7\,c^5\,x^3\,\left (7\,a^2\,d^2+21\,a\,b\,c\,d+12\,b^2\,c^2\right )+\frac {b^7\,d^5\,x^{15}\,\left (12\,a^2\,d^2+21\,a\,b\,c\,d+7\,b^2\,c^2\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 1163, normalized size = 5.82 \begin {gather*} a^{9} c^{7} x + \frac {b^{9} d^{7} x^{17}}{17} + x^{16} \left (\frac {9 a b^{8} d^{7}}{16} + \frac {7 b^{9} c d^{6}}{16}\right ) + x^{15} \left (\frac {12 a^{2} b^{7} d^{7}}{5} + \frac {21 a b^{8} c d^{6}}{5} + \frac {7 b^{9} c^{2} d^{5}}{5}\right ) + x^{14} \left (6 a^{3} b^{6} d^{7} + 18 a^{2} b^{7} c d^{6} + \frac {27 a b^{8} c^{2} d^{5}}{2} + \frac {5 b^{9} c^{3} d^{4}}{2}\right ) + x^{13} \left (\frac {126 a^{4} b^{5} d^{7}}{13} + \frac {588 a^{3} b^{6} c d^{6}}{13} + \frac {756 a^{2} b^{7} c^{2} d^{5}}{13} + \frac {315 a b^{8} c^{3} d^{4}}{13} + \frac {35 b^{9} c^{4} d^{3}}{13}\right ) + x^{12} \left (\frac {21 a^{5} b^{4} d^{7}}{2} + \frac {147 a^{4} b^{5} c d^{6}}{2} + 147 a^{3} b^{6} c^{2} d^{5} + 105 a^{2} b^{7} c^{3} d^{4} + \frac {105 a b^{8} c^{4} d^{3}}{4} + \frac {7 b^{9} c^{5} d^{2}}{4}\right ) + x^{11} \left (\frac {84 a^{6} b^{3} d^{7}}{11} + \frac {882 a^{5} b^{4} c d^{6}}{11} + \frac {2646 a^{4} b^{5} c^{2} d^{5}}{11} + \frac {2940 a^{3} b^{6} c^{3} d^{4}}{11} + \frac {1260 a^{2} b^{7} c^{4} d^{3}}{11} + \frac {189 a b^{8} c^{5} d^{2}}{11} + \frac {7 b^{9} c^{6} d}{11}\right ) + x^{10} \left (\frac {18 a^{7} b^{2} d^{7}}{5} + \frac {294 a^{6} b^{3} c d^{6}}{5} + \frac {1323 a^{5} b^{4} c^{2} d^{5}}{5} + 441 a^{4} b^{5} c^{3} d^{4} + 294 a^{3} b^{6} c^{4} d^{3} + \frac {378 a^{2} b^{7} c^{5} d^{2}}{5} + \frac {63 a b^{8} c^{6} d}{10} + \frac {b^{9} c^{7}}{10}\right ) + x^{9} \left (a^{8} b d^{7} + 28 a^{7} b^{2} c d^{6} + 196 a^{6} b^{3} c^{2} d^{5} + 490 a^{5} b^{4} c^{3} d^{4} + 490 a^{4} b^{5} c^{4} d^{3} + 196 a^{3} b^{6} c^{5} d^{2} + 28 a^{2} b^{7} c^{6} d + a b^{8} c^{7}\right ) + x^{8} \left (\frac {a^{9} d^{7}}{8} + \frac {63 a^{8} b c d^{6}}{8} + \frac {189 a^{7} b^{2} c^{2} d^{5}}{2} + \frac {735 a^{6} b^{3} c^{3} d^{4}}{2} + \frac {2205 a^{5} b^{4} c^{4} d^{3}}{4} + \frac {1323 a^{4} b^{5} c^{5} d^{2}}{4} + \frac {147 a^{3} b^{6} c^{6} d}{2} + \frac {9 a^{2} b^{7} c^{7}}{2}\right ) + x^{7} \left (a^{9} c d^{6} + 27 a^{8} b c^{2} d^{5} + 180 a^{7} b^{2} c^{3} d^{4} + 420 a^{6} b^{3} c^{4} d^{3} + 378 a^{5} b^{4} c^{5} d^{2} + 126 a^{4} b^{5} c^{6} d + 12 a^{3} b^{6} c^{7}\right ) + x^{6} \left (\frac {7 a^{9} c^{2} d^{5}}{2} + \frac {105 a^{8} b c^{3} d^{4}}{2} + 210 a^{7} b^{2} c^{4} d^{3} + 294 a^{6} b^{3} c^{5} d^{2} + 147 a^{5} b^{4} c^{6} d + 21 a^{4} b^{5} c^{7}\right ) + x^{5} \left (7 a^{9} c^{3} d^{4} + 63 a^{8} b c^{4} d^{3} + \frac {756 a^{7} b^{2} c^{5} d^{2}}{5} + \frac {588 a^{6} b^{3} c^{6} d}{5} + \frac {126 a^{5} b^{4} c^{7}}{5}\right ) + x^{4} \left (\frac {35 a^{9} c^{4} d^{3}}{4} + \frac {189 a^{8} b c^{5} d^{2}}{4} + 63 a^{7} b^{2} c^{6} d + 21 a^{6} b^{3} c^{7}\right ) + x^{3} \left (7 a^{9} c^{5} d^{2} + 21 a^{8} b c^{6} d + 12 a^{7} b^{2} c^{7}\right ) + x^{2} \left (\frac {7 a^{9} c^{6} d}{2} + \frac {9 a^{8} b c^{7}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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