Optimal. Leaf size=200 \[ \frac {(b c-a d)^7 (a+b x)^8}{8 b^8}+\frac {7 d (b c-a d)^6 (a+b x)^9}{9 b^8}+\frac {21 d^2 (b c-a d)^5 (a+b x)^{10}}{10 b^8}+\frac {35 d^3 (b c-a d)^4 (a+b x)^{11}}{11 b^8}+\frac {35 d^4 (b c-a d)^3 (a+b x)^{12}}{12 b^8}+\frac {21 d^5 (b c-a d)^2 (a+b x)^{13}}{13 b^8}+\frac {d^6 (b c-a d) (a+b x)^{14}}{2 b^8}+\frac {d^7 (a+b x)^{15}}{15 b^8} \]
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Rubi [A]
time = 0.31, 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 = {45}
\begin {gather*} \frac {d^6 (a+b x)^{14} (b c-a d)}{2 b^8}+\frac {21 d^5 (a+b x)^{13} (b c-a d)^2}{13 b^8}+\frac {35 d^4 (a+b x)^{12} (b c-a d)^3}{12 b^8}+\frac {35 d^3 (a+b x)^{11} (b c-a d)^4}{11 b^8}+\frac {21 d^2 (a+b x)^{10} (b c-a d)^5}{10 b^8}+\frac {7 d (a+b x)^9 (b c-a d)^6}{9 b^8}+\frac {(a+b x)^8 (b c-a d)^7}{8 b^8}+\frac {d^7 (a+b x)^{15}}{15 b^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (a+b x)^7 (c+d x)^7 \, dx &=\int \left (\frac {(b c-a d)^7 (a+b x)^7}{b^7}+\frac {7 d (b c-a d)^6 (a+b x)^8}{b^7}+\frac {21 d^2 (b c-a d)^5 (a+b x)^9}{b^7}+\frac {35 d^3 (b c-a d)^4 (a+b x)^{10}}{b^7}+\frac {35 d^4 (b c-a d)^3 (a+b x)^{11}}{b^7}+\frac {21 d^5 (b c-a d)^2 (a+b x)^{12}}{b^7}+\frac {7 d^6 (b c-a d) (a+b x)^{13}}{b^7}+\frac {d^7 (a+b x)^{14}}{b^7}\right ) \, dx\\ &=\frac {(b c-a d)^7 (a+b x)^8}{8 b^8}+\frac {7 d (b c-a d)^6 (a+b x)^9}{9 b^8}+\frac {21 d^2 (b c-a d)^5 (a+b x)^{10}}{10 b^8}+\frac {35 d^3 (b c-a d)^4 (a+b x)^{11}}{11 b^8}+\frac {35 d^4 (b c-a d)^3 (a+b x)^{12}}{12 b^8}+\frac {21 d^5 (b c-a d)^2 (a+b x)^{13}}{13 b^8}+\frac {d^6 (b c-a d) (a+b x)^{14}}{2 b^8}+\frac {d^7 (a+b x)^{15}}{15 b^8}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(785\) vs. \(2(200)=400\).
time = 0.04, size = 785, normalized size = 3.92 \begin {gather*} a^7 c^7 x+\frac {7}{2} a^6 c^6 (b c+a d) x^2+\frac {7}{3} a^5 c^5 \left (3 b^2 c^2+7 a b c d+3 a^2 d^2\right ) x^3+\frac {7}{4} a^4 c^4 \left (5 b^3 c^3+21 a b^2 c^2 d+21 a^2 b c d^2+5 a^3 d^3\right ) x^4+\frac {7}{5} a^3 c^3 \left (5 b^4 c^4+35 a b^3 c^3 d+63 a^2 b^2 c^2 d^2+35 a^3 b c d^3+5 a^4 d^4\right ) x^5+\frac {7}{6} a^2 c^2 \left (3 b^5 c^5+35 a b^4 c^4 d+105 a^2 b^3 c^3 d^2+105 a^3 b^2 c^2 d^3+35 a^4 b c d^4+3 a^5 d^5\right ) x^6+a c \left (b^6 c^6+21 a b^5 c^5 d+105 a^2 b^4 c^4 d^2+175 a^3 b^3 c^3 d^3+105 a^4 b^2 c^2 d^4+21 a^5 b c d^5+a^6 d^6\right ) x^7+\frac {1}{8} \left (b^7 c^7+49 a b^6 c^6 d+441 a^2 b^5 c^5 d^2+1225 a^3 b^4 c^4 d^3+1225 a^4 b^3 c^3 d^4+441 a^5 b^2 c^2 d^5+49 a^6 b c d^6+a^7 d^7\right ) x^8+\frac {7}{9} b d \left (b^6 c^6+21 a b^5 c^5 d+105 a^2 b^4 c^4 d^2+175 a^3 b^3 c^3 d^3+105 a^4 b^2 c^2 d^4+21 a^5 b c d^5+a^6 d^6\right ) x^9+\frac {7}{10} b^2 d^2 \left (3 b^5 c^5+35 a b^4 c^4 d+105 a^2 b^3 c^3 d^2+105 a^3 b^2 c^2 d^3+35 a^4 b c d^4+3 a^5 d^5\right ) x^{10}+\frac {7}{11} b^3 d^3 \left (5 b^4 c^4+35 a b^3 c^3 d+63 a^2 b^2 c^2 d^2+35 a^3 b c d^3+5 a^4 d^4\right ) x^{11}+\frac {7}{12} b^4 d^4 \left (5 b^3 c^3+21 a b^2 c^2 d+21 a^2 b c d^2+5 a^3 d^3\right ) x^{12}+\frac {7}{13} b^5 d^5 \left (3 b^2 c^2+7 a b c d+3 a^2 d^2\right ) x^{13}+\frac {1}{2} b^6 d^6 (b c+a d) x^{14}+\frac {1}{15} b^7 d^7 x^{15} \end {gather*}
Antiderivative was successfully verified.
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Mathics [B] Leaf count is larger than twice the leaf count of optimal. \(757\) vs. \(2(200)=400\).
time = 7.60, size = 755, normalized size = 3.78 \begin {gather*} \frac {x \left (51480 a^7 c^7+180180 a^6 c^6 x \left (a d+b c\right )+a^5 c^5 x^2 \left (360360 a^2 d^2+840840 a b c d+360360 b^2 c^2\right )+a^4 c^4 x^3 \left (450450 a^3 d^3+1891890 a^2 b c d^2+1891890 a b^2 c^2 d+450450 b^3 c^3\right )+a^3 c^3 x^4 \left (360360 a^4 d^4+2522520 a^3 b c d^3+4540536 a^2 b^2 c^2 d^2+2522520 a b^3 c^3 d+360360 b^4 c^4\right )+a^2 c^2 x^5 \left (180180 a^5 d^5+2102100 a^4 b c d^4+6306300 a^3 b^2 c^2 d^3+6306300 a^2 b^3 c^3 d^2+2102100 a b^4 c^4 d+180180 b^5 c^5\right )+51480 a c x^6 \left (a^6 d^6+21 a^5 b c d^5+105 a^4 b^2 c^2 d^4+175 a^3 b^3 c^3 d^3+105 a^2 b^4 c^4 d^2+21 a b^5 c^5 d+b^6 c^6\right )+x^7 \left (6435 a^7 d^7+315315 a^6 b c d^6+2837835 a^5 b^2 c^2 d^5+7882875 a^4 b^3 c^3 d^4+7882875 a^3 b^4 c^4 d^3+2837835 a^2 b^5 c^5 d^2+315315 a b^6 c^6 d+6435 b^7 c^7\right )+40040 b d x^8 \left (a^6 d^6+21 a^5 b c d^5+105 a^4 b^2 c^2 d^4+175 a^3 b^3 c^3 d^3+105 a^2 b^4 c^4 d^2+21 a b^5 c^5 d+b^6 c^6\right )+b^2 d^2 x^9 \left (108108 a^5 d^5+1261260 a^4 b c d^4+3783780 a^3 b^2 c^2 d^3+3783780 a^2 b^3 c^3 d^2+1261260 a b^4 c^4 d+108108 b^5 c^5\right )+b^3 d^3 x^{10} \left (163800 a^4 d^4+1146600 a^3 b c d^3+2063880 a^2 b^2 c^2 d^2+1146600 a b^3 c^3 d+163800 b^4 c^4\right )+b^4 d^4 x^{11} \left (150150 a^3 d^3+630630 a^2 b c d^2+630630 a b^2 c^2 d+150150 b^3 c^3\right )+b^5 d^5 x^{12} \left (83160 a^2 d^2+194040 a b c d+83160 b^2 c^2\right )+b^6 d^6 x^{13} \left (25740 a d+25740 b c\right )+3432 b^7 d^7 x^{14}\right )}{51480} \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. \(816\) vs.
\(2(184)=368\).
time = 0.15, size = 817, normalized size = 4.08
method | result | size |
norman | \(a^{7} c^{7} x +\left (\frac {7}{2} a^{7} c^{6} d +\frac {7}{2} a^{6} b \,c^{7}\right ) x^{2}+\left (7 a^{7} c^{5} d^{2}+\frac {49}{3} a^{6} b \,c^{6} d +7 a^{5} b^{2} c^{7}\right ) x^{3}+\left (\frac {35}{4} a^{7} c^{4} d^{3}+\frac {147}{4} a^{6} b \,c^{5} d^{2}+\frac {147}{4} a^{5} b^{2} c^{6} d +\frac {35}{4} a^{4} b^{3} c^{7}\right ) x^{4}+\left (7 a^{7} c^{3} d^{4}+49 a^{6} b \,c^{4} d^{3}+\frac {441}{5} a^{5} b^{2} c^{5} d^{2}+49 a^{4} b^{3} c^{6} d +7 a^{3} b^{4} c^{7}\right ) x^{5}+\left (\frac {7}{2} a^{7} c^{2} d^{5}+\frac {245}{6} a^{6} b \,c^{3} d^{4}+\frac {245}{2} a^{5} b^{2} c^{4} d^{3}+\frac {245}{2} a^{4} b^{3} c^{5} d^{2}+\frac {245}{6} a^{3} b^{4} c^{6} d +\frac {7}{2} a^{2} b^{5} c^{7}\right ) x^{6}+\left (a^{7} c \,d^{6}+21 a^{6} b \,c^{2} d^{5}+105 a^{5} b^{2} c^{3} d^{4}+175 a^{4} b^{3} c^{4} d^{3}+105 a^{3} b^{4} c^{5} d^{2}+21 a^{2} b^{5} c^{6} d +a \,b^{6} c^{7}\right ) x^{7}+\left (\frac {1}{8} a^{7} d^{7}+\frac {49}{8} a^{6} b c \,d^{6}+\frac {441}{8} a^{5} b^{2} c^{2} d^{5}+\frac {1225}{8} a^{4} b^{3} c^{3} d^{4}+\frac {1225}{8} a^{3} b^{4} c^{4} d^{3}+\frac {441}{8} a^{2} b^{5} c^{5} d^{2}+\frac {49}{8} a \,b^{6} c^{6} d +\frac {1}{8} b^{7} c^{7}\right ) x^{8}+\left (\frac {7}{9} a^{6} b \,d^{7}+\frac {49}{3} a^{5} b^{2} c \,d^{6}+\frac {245}{3} a^{4} b^{3} c^{2} d^{5}+\frac {1225}{9} a^{3} b^{4} c^{3} d^{4}+\frac {245}{3} a^{2} b^{5} c^{4} d^{3}+\frac {49}{3} a \,b^{6} c^{5} d^{2}+\frac {7}{9} b^{7} c^{6} d \right ) x^{9}+\left (\frac {21}{10} a^{5} b^{2} d^{7}+\frac {49}{2} a^{4} b^{3} c \,d^{6}+\frac {147}{2} a^{3} b^{4} c^{2} d^{5}+\frac {147}{2} a^{2} b^{5} c^{3} d^{4}+\frac {49}{2} a \,b^{6} c^{4} d^{3}+\frac {21}{10} b^{7} c^{5} d^{2}\right ) x^{10}+\left (\frac {35}{11} a^{4} b^{3} d^{7}+\frac {245}{11} a^{3} b^{4} c \,d^{6}+\frac {441}{11} a^{2} b^{5} c^{2} d^{5}+\frac {245}{11} a \,b^{6} c^{3} d^{4}+\frac {35}{11} b^{7} c^{4} d^{3}\right ) x^{11}+\left (\frac {35}{12} a^{3} b^{4} d^{7}+\frac {49}{4} a^{2} b^{5} c \,d^{6}+\frac {49}{4} a \,b^{6} c^{2} d^{5}+\frac {35}{12} b^{7} c^{3} d^{4}\right ) x^{12}+\left (\frac {21}{13} a^{2} b^{5} d^{7}+\frac {49}{13} a \,b^{6} c \,d^{6}+\frac {21}{13} b^{7} c^{2} d^{5}\right ) x^{13}+\left (\frac {1}{2} a \,b^{6} d^{7}+\frac {1}{2} b^{7} c \,d^{6}\right ) x^{14}+\frac {b^{7} d^{7} x^{15}}{15}\) | \(804\) |
default | \(\frac {b^{7} d^{7} x^{15}}{15}+\frac {\left (7 a \,b^{6} d^{7}+7 b^{7} c \,d^{6}\right ) x^{14}}{14}+\frac {\left (21 a^{2} b^{5} d^{7}+49 a \,b^{6} c \,d^{6}+21 b^{7} c^{2} d^{5}\right ) x^{13}}{13}+\frac {\left (35 a^{3} b^{4} d^{7}+147 a^{2} b^{5} c \,d^{6}+147 a \,b^{6} c^{2} d^{5}+35 b^{7} c^{3} d^{4}\right ) x^{12}}{12}+\frac {\left (35 a^{4} b^{3} d^{7}+245 a^{3} b^{4} c \,d^{6}+441 a^{2} b^{5} c^{2} d^{5}+245 a \,b^{6} c^{3} d^{4}+35 b^{7} c^{4} d^{3}\right ) x^{11}}{11}+\frac {\left (21 a^{5} b^{2} d^{7}+245 a^{4} b^{3} c \,d^{6}+735 a^{3} b^{4} c^{2} d^{5}+735 a^{2} b^{5} c^{3} d^{4}+245 a \,b^{6} c^{4} d^{3}+21 b^{7} c^{5} d^{2}\right ) x^{10}}{10}+\frac {\left (7 a^{6} b \,d^{7}+147 a^{5} b^{2} c \,d^{6}+735 a^{4} b^{3} c^{2} d^{5}+1225 a^{3} b^{4} c^{3} d^{4}+735 a^{2} b^{5} c^{4} d^{3}+147 a \,b^{6} c^{5} d^{2}+7 b^{7} c^{6} d \right ) x^{9}}{9}+\frac {\left (a^{7} d^{7}+49 a^{6} b c \,d^{6}+441 a^{5} b^{2} c^{2} d^{5}+1225 a^{4} b^{3} c^{3} d^{4}+1225 a^{3} b^{4} c^{4} d^{3}+441 a^{2} b^{5} c^{5} d^{2}+49 a \,b^{6} c^{6} d +b^{7} c^{7}\right ) x^{8}}{8}+\frac {\left (7 a^{7} c \,d^{6}+147 a^{6} b \,c^{2} d^{5}+735 a^{5} b^{2} c^{3} d^{4}+1225 a^{4} b^{3} c^{4} d^{3}+735 a^{3} b^{4} c^{5} d^{2}+147 a^{2} b^{5} c^{6} d +7 a \,b^{6} c^{7}\right ) x^{7}}{7}+\frac {\left (21 a^{7} c^{2} d^{5}+245 a^{6} b \,c^{3} d^{4}+735 a^{5} b^{2} c^{4} d^{3}+735 a^{4} b^{3} c^{5} d^{2}+245 a^{3} b^{4} c^{6} d +21 a^{2} b^{5} c^{7}\right ) x^{6}}{6}+\frac {\left (35 a^{7} c^{3} d^{4}+245 a^{6} b \,c^{4} d^{3}+441 a^{5} b^{2} c^{5} d^{2}+245 a^{4} b^{3} c^{6} d +35 a^{3} b^{4} c^{7}\right ) x^{5}}{5}+\frac {\left (35 a^{7} c^{4} d^{3}+147 a^{6} b \,c^{5} d^{2}+147 a^{5} b^{2} c^{6} d +35 a^{4} b^{3} c^{7}\right ) x^{4}}{4}+\frac {\left (21 a^{7} c^{5} d^{2}+49 a^{6} b \,c^{6} d +21 a^{5} b^{2} c^{7}\right ) x^{3}}{3}+\frac {\left (7 a^{7} c^{6} d +7 a^{6} b \,c^{7}\right ) x^{2}}{2}+a^{7} c^{7} x\) | \(817\) |
gosper | \(7 x^{5} a^{3} b^{4} c^{7}+\frac {7}{2} x^{6} a^{7} c^{2} d^{5}+\frac {7}{2} x^{6} a^{2} b^{5} c^{7}+\frac {7}{9} x^{9} a^{6} b \,d^{7}+\frac {7}{9} x^{9} b^{7} c^{6} d +\frac {21}{10} x^{10} a^{5} b^{2} d^{7}+\frac {21}{10} x^{10} b^{7} c^{5} d^{2}+\frac {35}{11} x^{11} a^{4} b^{3} d^{7}+\frac {35}{11} x^{11} b^{7} c^{4} d^{3}+\frac {35}{12} x^{12} a^{3} b^{4} d^{7}+\frac {35}{12} x^{12} b^{7} c^{3} d^{4}+\frac {21}{13} x^{13} a^{2} b^{5} d^{7}+\frac {7}{2} x^{2} a^{6} b \,c^{7}+7 x^{3} a^{7} c^{5} d^{2}+\frac {1}{2} x^{14} b^{7} c \,d^{6}+a^{7} c \,d^{6} x^{7}+a \,b^{6} c^{7} x^{7}+\frac {21}{13} x^{13} b^{7} c^{2} d^{5}+\frac {1}{2} x^{14} a \,b^{6} d^{7}+\frac {35}{4} x^{4} a^{7} c^{4} d^{3}+\frac {35}{4} x^{4} a^{4} b^{3} c^{7}+7 x^{5} a^{7} c^{3} d^{4}+7 x^{3} a^{5} b^{2} c^{7}+\frac {7}{2} x^{2} a^{7} c^{6} d +\frac {1}{8} x^{8} a^{7} d^{7}+\frac {1}{8} x^{8} b^{7} c^{7}+\frac {1}{15} b^{7} d^{7} x^{15}+a^{7} c^{7} x +21 a^{2} b^{5} c^{6} d \,x^{7}+\frac {245}{11} x^{11} a^{3} b^{4} c \,d^{6}+\frac {441}{11} x^{11} a^{2} b^{5} c^{2} d^{5}+\frac {245}{11} x^{11} a \,b^{6} c^{3} d^{4}+\frac {49}{4} x^{12} a^{2} b^{5} c \,d^{6}+\frac {49}{4} x^{12} a \,b^{6} c^{2} d^{5}+\frac {49}{13} x^{13} a \,b^{6} c \,d^{6}+21 a^{6} b \,c^{2} d^{5} x^{7}+105 a^{5} b^{2} c^{3} d^{4} x^{7}+175 a^{4} b^{3} c^{4} d^{3} x^{7}+105 a^{3} b^{4} c^{5} d^{2} x^{7}+\frac {147}{2} x^{10} a^{3} b^{4} c^{2} d^{5}+\frac {147}{2} x^{10} a^{2} b^{5} c^{3} d^{4}+\frac {49}{2} x^{10} a \,b^{6} c^{4} d^{3}+\frac {441}{8} x^{8} a^{2} b^{5} c^{5} d^{2}+\frac {49}{8} x^{8} a \,b^{6} c^{6} d +\frac {49}{3} x^{9} a^{5} b^{2} c \,d^{6}+\frac {245}{3} x^{9} a^{4} b^{3} c^{2} d^{5}+\frac {1225}{9} x^{9} a^{3} b^{4} c^{3} d^{4}+\frac {245}{3} x^{9} a^{2} b^{5} c^{4} d^{3}+\frac {49}{3} x^{9} a \,b^{6} c^{5} d^{2}+\frac {49}{2} x^{10} a^{4} b^{3} c \,d^{6}+\frac {49}{3} x^{3} a^{6} b \,c^{6} d +\frac {147}{4} x^{4} a^{6} b \,c^{5} d^{2}+\frac {147}{4} x^{4} a^{5} b^{2} c^{6} d +49 x^{5} a^{6} b \,c^{4} d^{3}+\frac {441}{5} x^{5} a^{5} b^{2} c^{5} d^{2}+49 x^{5} a^{4} b^{3} c^{6} d +\frac {245}{6} x^{6} a^{6} b \,c^{3} d^{4}+\frac {245}{2} x^{6} a^{5} b^{2} c^{4} d^{3}+\frac {245}{2} x^{6} a^{4} b^{3} c^{5} d^{2}+\frac {245}{6} x^{6} a^{3} b^{4} c^{6} d +\frac {49}{8} x^{8} a^{6} b c \,d^{6}+\frac {441}{8} x^{8} a^{5} b^{2} c^{2} d^{5}+\frac {1225}{8} x^{8} a^{4} b^{3} c^{3} d^{4}+\frac {1225}{8} x^{8} a^{3} b^{4} c^{4} d^{3}\) | \(925\) |
risch | \(7 x^{5} a^{3} b^{4} c^{7}+\frac {7}{2} x^{6} a^{7} c^{2} d^{5}+\frac {7}{2} x^{6} a^{2} b^{5} c^{7}+\frac {7}{9} x^{9} a^{6} b \,d^{7}+\frac {7}{9} x^{9} b^{7} c^{6} d +\frac {21}{10} x^{10} a^{5} b^{2} d^{7}+\frac {21}{10} x^{10} b^{7} c^{5} d^{2}+\frac {35}{11} x^{11} a^{4} b^{3} d^{7}+\frac {35}{11} x^{11} b^{7} c^{4} d^{3}+\frac {35}{12} x^{12} a^{3} b^{4} d^{7}+\frac {35}{12} x^{12} b^{7} c^{3} d^{4}+\frac {21}{13} x^{13} a^{2} b^{5} d^{7}+\frac {7}{2} x^{2} a^{6} b \,c^{7}+7 x^{3} a^{7} c^{5} d^{2}+\frac {1}{2} x^{14} b^{7} c \,d^{6}+a^{7} c \,d^{6} x^{7}+a \,b^{6} c^{7} x^{7}+\frac {21}{13} x^{13} b^{7} c^{2} d^{5}+\frac {1}{2} x^{14} a \,b^{6} d^{7}+\frac {35}{4} x^{4} a^{7} c^{4} d^{3}+\frac {35}{4} x^{4} a^{4} b^{3} c^{7}+7 x^{5} a^{7} c^{3} d^{4}+7 x^{3} a^{5} b^{2} c^{7}+\frac {7}{2} x^{2} a^{7} c^{6} d +\frac {1}{8} x^{8} a^{7} d^{7}+\frac {1}{8} x^{8} b^{7} c^{7}+\frac {1}{15} b^{7} d^{7} x^{15}+a^{7} c^{7} x +21 a^{2} b^{5} c^{6} d \,x^{7}+\frac {245}{11} x^{11} a^{3} b^{4} c \,d^{6}+\frac {441}{11} x^{11} a^{2} b^{5} c^{2} d^{5}+\frac {245}{11} x^{11} a \,b^{6} c^{3} d^{4}+\frac {49}{4} x^{12} a^{2} b^{5} c \,d^{6}+\frac {49}{4} x^{12} a \,b^{6} c^{2} d^{5}+\frac {49}{13} x^{13} a \,b^{6} c \,d^{6}+21 a^{6} b \,c^{2} d^{5} x^{7}+105 a^{5} b^{2} c^{3} d^{4} x^{7}+175 a^{4} b^{3} c^{4} d^{3} x^{7}+105 a^{3} b^{4} c^{5} d^{2} x^{7}+\frac {147}{2} x^{10} a^{3} b^{4} c^{2} d^{5}+\frac {147}{2} x^{10} a^{2} b^{5} c^{3} d^{4}+\frac {49}{2} x^{10} a \,b^{6} c^{4} d^{3}+\frac {441}{8} x^{8} a^{2} b^{5} c^{5} d^{2}+\frac {49}{8} x^{8} a \,b^{6} c^{6} d +\frac {49}{3} x^{9} a^{5} b^{2} c \,d^{6}+\frac {245}{3} x^{9} a^{4} b^{3} c^{2} d^{5}+\frac {1225}{9} x^{9} a^{3} b^{4} c^{3} d^{4}+\frac {245}{3} x^{9} a^{2} b^{5} c^{4} d^{3}+\frac {49}{3} x^{9} a \,b^{6} c^{5} d^{2}+\frac {49}{2} x^{10} a^{4} b^{3} c \,d^{6}+\frac {49}{3} x^{3} a^{6} b \,c^{6} d +\frac {147}{4} x^{4} a^{6} b \,c^{5} d^{2}+\frac {147}{4} x^{4} a^{5} b^{2} c^{6} d +49 x^{5} a^{6} b \,c^{4} d^{3}+\frac {441}{5} x^{5} a^{5} b^{2} c^{5} d^{2}+49 x^{5} a^{4} b^{3} c^{6} d +\frac {245}{6} x^{6} a^{6} b \,c^{3} d^{4}+\frac {245}{2} x^{6} a^{5} b^{2} c^{4} d^{3}+\frac {245}{2} x^{6} a^{4} b^{3} c^{5} d^{2}+\frac {245}{6} x^{6} a^{3} b^{4} c^{6} d +\frac {49}{8} x^{8} a^{6} b c \,d^{6}+\frac {441}{8} x^{8} a^{5} b^{2} c^{2} d^{5}+\frac {1225}{8} x^{8} a^{4} b^{3} c^{3} d^{4}+\frac {1225}{8} x^{8} a^{3} b^{4} c^{4} d^{3}\) | \(925\) |
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. 807 vs.
\(2 (184) = 368\).
time = 0.27, size = 807, normalized size = 4.04 \begin {gather*} \frac {1}{15} \, b^{7} d^{7} x^{15} + a^{7} c^{7} x + \frac {1}{2} \, {\left (b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{14} + \frac {7}{13} \, {\left (3 \, b^{7} c^{2} d^{5} + 7 \, a b^{6} c d^{6} + 3 \, a^{2} b^{5} d^{7}\right )} x^{13} + \frac {7}{12} \, {\left (5 \, b^{7} c^{3} d^{4} + 21 \, a b^{6} c^{2} d^{5} + 21 \, a^{2} b^{5} c d^{6} + 5 \, a^{3} b^{4} d^{7}\right )} x^{12} + \frac {7}{11} \, {\left (5 \, b^{7} c^{4} d^{3} + 35 \, a b^{6} c^{3} d^{4} + 63 \, a^{2} b^{5} c^{2} d^{5} + 35 \, a^{3} b^{4} c d^{6} + 5 \, a^{4} b^{3} d^{7}\right )} x^{11} + \frac {7}{10} \, {\left (3 \, b^{7} c^{5} d^{2} + 35 \, a b^{6} c^{4} d^{3} + 105 \, a^{2} b^{5} c^{3} d^{4} + 105 \, a^{3} b^{4} c^{2} d^{5} + 35 \, a^{4} b^{3} c d^{6} + 3 \, a^{5} b^{2} d^{7}\right )} x^{10} + \frac {7}{9} \, {\left (b^{7} c^{6} d + 21 \, a b^{6} c^{5} d^{2} + 105 \, a^{2} b^{5} c^{4} d^{3} + 175 \, a^{3} b^{4} c^{3} d^{4} + 105 \, a^{4} b^{3} c^{2} d^{5} + 21 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x^{9} + \frac {1}{8} \, {\left (b^{7} c^{7} + 49 \, a b^{6} c^{6} d + 441 \, a^{2} b^{5} c^{5} d^{2} + 1225 \, a^{3} b^{4} c^{4} d^{3} + 1225 \, a^{4} b^{3} c^{3} d^{4} + 441 \, a^{5} b^{2} c^{2} d^{5} + 49 \, a^{6} b c d^{6} + a^{7} d^{7}\right )} x^{8} + {\left (a b^{6} c^{7} + 21 \, a^{2} b^{5} c^{6} d + 105 \, a^{3} b^{4} c^{5} d^{2} + 175 \, a^{4} b^{3} c^{4} d^{3} + 105 \, a^{5} b^{2} c^{3} d^{4} + 21 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right )} x^{7} + \frac {7}{6} \, {\left (3 \, a^{2} b^{5} c^{7} + 35 \, a^{3} b^{4} c^{6} d + 105 \, a^{4} b^{3} c^{5} d^{2} + 105 \, a^{5} b^{2} c^{4} d^{3} + 35 \, a^{6} b c^{3} d^{4} + 3 \, a^{7} c^{2} d^{5}\right )} x^{6} + \frac {7}{5} \, {\left (5 \, a^{3} b^{4} c^{7} + 35 \, a^{4} b^{3} c^{6} d + 63 \, a^{5} b^{2} c^{5} d^{2} + 35 \, a^{6} b c^{4} d^{3} + 5 \, a^{7} c^{3} d^{4}\right )} x^{5} + \frac {7}{4} \, {\left (5 \, a^{4} b^{3} c^{7} + 21 \, a^{5} b^{2} c^{6} d + 21 \, a^{6} b c^{5} d^{2} + 5 \, a^{7} c^{4} d^{3}\right )} x^{4} + \frac {7}{3} \, {\left (3 \, a^{5} b^{2} c^{7} + 7 \, a^{6} b c^{6} d + 3 \, a^{7} c^{5} d^{2}\right )} x^{3} + \frac {7}{2} \, {\left (a^{6} b c^{7} + a^{7} c^{6} 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. 807 vs.
\(2 (184) = 368\).
time = 0.29, size = 807, normalized size = 4.04 \begin {gather*} \frac {1}{15} \, b^{7} d^{7} x^{15} + a^{7} c^{7} x + \frac {1}{2} \, {\left (b^{7} c d^{6} + a b^{6} d^{7}\right )} x^{14} + \frac {7}{13} \, {\left (3 \, b^{7} c^{2} d^{5} + 7 \, a b^{6} c d^{6} + 3 \, a^{2} b^{5} d^{7}\right )} x^{13} + \frac {7}{12} \, {\left (5 \, b^{7} c^{3} d^{4} + 21 \, a b^{6} c^{2} d^{5} + 21 \, a^{2} b^{5} c d^{6} + 5 \, a^{3} b^{4} d^{7}\right )} x^{12} + \frac {7}{11} \, {\left (5 \, b^{7} c^{4} d^{3} + 35 \, a b^{6} c^{3} d^{4} + 63 \, a^{2} b^{5} c^{2} d^{5} + 35 \, a^{3} b^{4} c d^{6} + 5 \, a^{4} b^{3} d^{7}\right )} x^{11} + \frac {7}{10} \, {\left (3 \, b^{7} c^{5} d^{2} + 35 \, a b^{6} c^{4} d^{3} + 105 \, a^{2} b^{5} c^{3} d^{4} + 105 \, a^{3} b^{4} c^{2} d^{5} + 35 \, a^{4} b^{3} c d^{6} + 3 \, a^{5} b^{2} d^{7}\right )} x^{10} + \frac {7}{9} \, {\left (b^{7} c^{6} d + 21 \, a b^{6} c^{5} d^{2} + 105 \, a^{2} b^{5} c^{4} d^{3} + 175 \, a^{3} b^{4} c^{3} d^{4} + 105 \, a^{4} b^{3} c^{2} d^{5} + 21 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x^{9} + \frac {1}{8} \, {\left (b^{7} c^{7} + 49 \, a b^{6} c^{6} d + 441 \, a^{2} b^{5} c^{5} d^{2} + 1225 \, a^{3} b^{4} c^{4} d^{3} + 1225 \, a^{4} b^{3} c^{3} d^{4} + 441 \, a^{5} b^{2} c^{2} d^{5} + 49 \, a^{6} b c d^{6} + a^{7} d^{7}\right )} x^{8} + {\left (a b^{6} c^{7} + 21 \, a^{2} b^{5} c^{6} d + 105 \, a^{3} b^{4} c^{5} d^{2} + 175 \, a^{4} b^{3} c^{4} d^{3} + 105 \, a^{5} b^{2} c^{3} d^{4} + 21 \, a^{6} b c^{2} d^{5} + a^{7} c d^{6}\right )} x^{7} + \frac {7}{6} \, {\left (3 \, a^{2} b^{5} c^{7} + 35 \, a^{3} b^{4} c^{6} d + 105 \, a^{4} b^{3} c^{5} d^{2} + 105 \, a^{5} b^{2} c^{4} d^{3} + 35 \, a^{6} b c^{3} d^{4} + 3 \, a^{7} c^{2} d^{5}\right )} x^{6} + \frac {7}{5} \, {\left (5 \, a^{3} b^{4} c^{7} + 35 \, a^{4} b^{3} c^{6} d + 63 \, a^{5} b^{2} c^{5} d^{2} + 35 \, a^{6} b c^{4} d^{3} + 5 \, a^{7} c^{3} d^{4}\right )} x^{5} + \frac {7}{4} \, {\left (5 \, a^{4} b^{3} c^{7} + 21 \, a^{5} b^{2} c^{6} d + 21 \, a^{6} b c^{5} d^{2} + 5 \, a^{7} c^{4} d^{3}\right )} x^{4} + \frac {7}{3} \, {\left (3 \, a^{5} b^{2} c^{7} + 7 \, a^{6} b c^{6} d + 3 \, a^{7} c^{5} d^{2}\right )} x^{3} + \frac {7}{2} \, {\left (a^{6} b c^{7} + a^{7} c^{6} 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. 935 vs.
\(2 (182) = 364\).
time = 0.09, size = 935, normalized size = 4.68 \begin {gather*} a^{7} c^{7} x + \frac {b^{7} d^{7} x^{15}}{15} + x^{14} \left (\frac {a b^{6} d^{7}}{2} + \frac {b^{7} c d^{6}}{2}\right ) + x^{13} \cdot \left (\frac {21 a^{2} b^{5} d^{7}}{13} + \frac {49 a b^{6} c d^{6}}{13} + \frac {21 b^{7} c^{2} d^{5}}{13}\right ) + x^{12} \cdot \left (\frac {35 a^{3} b^{4} d^{7}}{12} + \frac {49 a^{2} b^{5} c d^{6}}{4} + \frac {49 a b^{6} c^{2} d^{5}}{4} + \frac {35 b^{7} c^{3} d^{4}}{12}\right ) + x^{11} \cdot \left (\frac {35 a^{4} b^{3} d^{7}}{11} + \frac {245 a^{3} b^{4} c d^{6}}{11} + \frac {441 a^{2} b^{5} c^{2} d^{5}}{11} + \frac {245 a b^{6} c^{3} d^{4}}{11} + \frac {35 b^{7} c^{4} d^{3}}{11}\right ) + x^{10} \cdot \left (\frac {21 a^{5} b^{2} d^{7}}{10} + \frac {49 a^{4} b^{3} c d^{6}}{2} + \frac {147 a^{3} b^{4} c^{2} d^{5}}{2} + \frac {147 a^{2} b^{5} c^{3} d^{4}}{2} + \frac {49 a b^{6} c^{4} d^{3}}{2} + \frac {21 b^{7} c^{5} d^{2}}{10}\right ) + x^{9} \cdot \left (\frac {7 a^{6} b d^{7}}{9} + \frac {49 a^{5} b^{2} c d^{6}}{3} + \frac {245 a^{4} b^{3} c^{2} d^{5}}{3} + \frac {1225 a^{3} b^{4} c^{3} d^{4}}{9} + \frac {245 a^{2} b^{5} c^{4} d^{3}}{3} + \frac {49 a b^{6} c^{5} d^{2}}{3} + \frac {7 b^{7} c^{6} d}{9}\right ) + x^{8} \left (\frac {a^{7} d^{7}}{8} + \frac {49 a^{6} b c d^{6}}{8} + \frac {441 a^{5} b^{2} c^{2} d^{5}}{8} + \frac {1225 a^{4} b^{3} c^{3} d^{4}}{8} + \frac {1225 a^{3} b^{4} c^{4} d^{3}}{8} + \frac {441 a^{2} b^{5} c^{5} d^{2}}{8} + \frac {49 a b^{6} c^{6} d}{8} + \frac {b^{7} c^{7}}{8}\right ) + x^{7} \left (a^{7} c d^{6} + 21 a^{6} b c^{2} d^{5} + 105 a^{5} b^{2} c^{3} d^{4} + 175 a^{4} b^{3} c^{4} d^{3} + 105 a^{3} b^{4} c^{5} d^{2} + 21 a^{2} b^{5} c^{6} d + a b^{6} c^{7}\right ) + x^{6} \cdot \left (\frac {7 a^{7} c^{2} d^{5}}{2} + \frac {245 a^{6} b c^{3} d^{4}}{6} + \frac {245 a^{5} b^{2} c^{4} d^{3}}{2} + \frac {245 a^{4} b^{3} c^{5} d^{2}}{2} + \frac {245 a^{3} b^{4} c^{6} d}{6} + \frac {7 a^{2} b^{5} c^{7}}{2}\right ) + x^{5} \cdot \left (7 a^{7} c^{3} d^{4} + 49 a^{6} b c^{4} d^{3} + \frac {441 a^{5} b^{2} c^{5} d^{2}}{5} + 49 a^{4} b^{3} c^{6} d + 7 a^{3} b^{4} c^{7}\right ) + x^{4} \cdot \left (\frac {35 a^{7} c^{4} d^{3}}{4} + \frac {147 a^{6} b c^{5} d^{2}}{4} + \frac {147 a^{5} b^{2} c^{6} d}{4} + \frac {35 a^{4} b^{3} c^{7}}{4}\right ) + x^{3} \cdot \left (7 a^{7} c^{5} d^{2} + \frac {49 a^{6} b c^{6} d}{3} + 7 a^{5} b^{2} c^{7}\right ) + x^{2} \cdot \left (\frac {7 a^{7} c^{6} d}{2} + \frac {7 a^{6} b c^{7}}{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. 924 vs.
\(2 (184) = 368\).
time = 0.00, size = 1024, normalized size = 5.12 \begin {gather*} \frac {1}{15} x^{15} b^{7} d^{7}+\frac {1}{2} x^{14} b^{7} d^{6} c+\frac {1}{2} x^{14} b^{6} a d^{7}+\frac {21}{13} x^{13} b^{7} d^{5} c^{2}+\frac {49}{13} x^{13} b^{6} a d^{6} c+\frac {21}{13} x^{13} b^{5} a^{2} d^{7}+\frac {35}{12} x^{12} b^{7} d^{4} c^{3}+\frac {49}{4} x^{12} b^{6} a d^{5} c^{2}+\frac {49}{4} x^{12} b^{5} a^{2} d^{6} c+\frac {35}{12} x^{12} b^{4} a^{3} d^{7}+\frac {35}{11} x^{11} b^{7} d^{3} c^{4}+\frac {245}{11} x^{11} b^{6} a d^{4} c^{3}+\frac {441}{11} x^{11} b^{5} a^{2} d^{5} c^{2}+\frac {245}{11} x^{11} b^{4} a^{3} d^{6} c+\frac {35}{11} x^{11} b^{3} a^{4} d^{7}+\frac {21}{10} x^{10} b^{7} d^{2} c^{5}+\frac {49}{2} x^{10} b^{6} a d^{3} c^{4}+\frac {147}{2} x^{10} b^{5} a^{2} d^{4} c^{3}+\frac {147}{2} x^{10} b^{4} a^{3} d^{5} c^{2}+\frac {49}{2} x^{10} b^{3} a^{4} d^{6} c+\frac {21}{10} x^{10} b^{2} a^{5} d^{7}+\frac {7}{9} x^{9} b^{7} d c^{6}+\frac {49}{3} x^{9} b^{6} a d^{2} c^{5}+\frac {245}{3} x^{9} b^{5} a^{2} d^{3} c^{4}+\frac {1225}{9} x^{9} b^{4} a^{3} d^{4} c^{3}+\frac {245}{3} x^{9} b^{3} a^{4} d^{5} c^{2}+\frac {49}{3} x^{9} b^{2} a^{5} d^{6} c+\frac {7}{9} x^{9} b a^{6} d^{7}+\frac {1}{8} x^{8} b^{7} c^{7}+\frac {49}{8} x^{8} b^{6} a d c^{6}+\frac {441}{8} x^{8} b^{5} a^{2} d^{2} c^{5}+\frac {1225}{8} x^{8} b^{4} a^{3} d^{3} c^{4}+\frac {1225}{8} x^{8} b^{3} a^{4} d^{4} c^{3}+\frac {441}{8} x^{8} b^{2} a^{5} d^{5} c^{2}+\frac {49}{8} x^{8} b a^{6} d^{6} c+\frac {1}{8} x^{8} a^{7} d^{7}+x^{7} b^{6} a c^{7}+21 x^{7} b^{5} a^{2} d c^{6}+105 x^{7} b^{4} a^{3} d^{2} c^{5}+175 x^{7} b^{3} a^{4} d^{3} c^{4}+105 x^{7} b^{2} a^{5} d^{4} c^{3}+21 x^{7} b a^{6} d^{5} c^{2}+x^{7} a^{7} d^{6} c+\frac {7}{2} x^{6} b^{5} a^{2} c^{7}+\frac {245}{6} x^{6} b^{4} a^{3} d c^{6}+\frac {245}{2} x^{6} b^{3} a^{4} d^{2} c^{5}+\frac {245}{2} x^{6} b^{2} a^{5} d^{3} c^{4}+\frac {245}{6} x^{6} b a^{6} d^{4} c^{3}+\frac {7}{2} x^{6} a^{7} d^{5} c^{2}+7 x^{5} b^{4} a^{3} c^{7}+49 x^{5} b^{3} a^{4} d c^{6}+\frac {441}{5} x^{5} b^{2} a^{5} d^{2} c^{5}+49 x^{5} b a^{6} d^{3} c^{4}+7 x^{5} a^{7} d^{4} c^{3}+\frac {35}{4} x^{4} b^{3} a^{4} c^{7}+\frac {147}{4} x^{4} b^{2} a^{5} d c^{6}+\frac {147}{4} x^{4} b a^{6} d^{2} c^{5}+\frac {35}{4} x^{4} a^{7} d^{3} c^{4}+7 x^{3} b^{2} a^{5} c^{7}+\frac {49}{3} x^{3} b a^{6} d c^{6}+7 x^{3} a^{7} d^{2} c^{5}+\frac {7}{2} x^{2} b a^{6} c^{7}+\frac {7}{2} x^{2} a^{7} d c^{6}+x a^{7} c^{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.40, size = 781, normalized size = 3.90 \begin {gather*} x^8\,\left (\frac {a^7\,d^7}{8}+\frac {49\,a^6\,b\,c\,d^6}{8}+\frac {441\,a^5\,b^2\,c^2\,d^5}{8}+\frac {1225\,a^4\,b^3\,c^3\,d^4}{8}+\frac {1225\,a^3\,b^4\,c^4\,d^3}{8}+\frac {441\,a^2\,b^5\,c^5\,d^2}{8}+\frac {49\,a\,b^6\,c^6\,d}{8}+\frac {b^7\,c^7}{8}\right )+x^5\,\left (7\,a^7\,c^3\,d^4+49\,a^6\,b\,c^4\,d^3+\frac {441\,a^5\,b^2\,c^5\,d^2}{5}+49\,a^4\,b^3\,c^6\,d+7\,a^3\,b^4\,c^7\right )+x^{11}\,\left (\frac {35\,a^4\,b^3\,d^7}{11}+\frac {245\,a^3\,b^4\,c\,d^6}{11}+\frac {441\,a^2\,b^5\,c^2\,d^5}{11}+\frac {245\,a\,b^6\,c^3\,d^4}{11}+\frac {35\,b^7\,c^4\,d^3}{11}\right )+x^7\,\left (a^7\,c\,d^6+21\,a^6\,b\,c^2\,d^5+105\,a^5\,b^2\,c^3\,d^4+175\,a^4\,b^3\,c^4\,d^3+105\,a^3\,b^4\,c^5\,d^2+21\,a^2\,b^5\,c^6\,d+a\,b^6\,c^7\right )+x^9\,\left (\frac {7\,a^6\,b\,d^7}{9}+\frac {49\,a^5\,b^2\,c\,d^6}{3}+\frac {245\,a^4\,b^3\,c^2\,d^5}{3}+\frac {1225\,a^3\,b^4\,c^3\,d^4}{9}+\frac {245\,a^2\,b^5\,c^4\,d^3}{3}+\frac {49\,a\,b^6\,c^5\,d^2}{3}+\frac {7\,b^7\,c^6\,d}{9}\right )+x^6\,\left (\frac {7\,a^7\,c^2\,d^5}{2}+\frac {245\,a^6\,b\,c^3\,d^4}{6}+\frac {245\,a^5\,b^2\,c^4\,d^3}{2}+\frac {245\,a^4\,b^3\,c^5\,d^2}{2}+\frac {245\,a^3\,b^4\,c^6\,d}{6}+\frac {7\,a^2\,b^5\,c^7}{2}\right )+x^{10}\,\left (\frac {21\,a^5\,b^2\,d^7}{10}+\frac {49\,a^4\,b^3\,c\,d^6}{2}+\frac {147\,a^3\,b^4\,c^2\,d^5}{2}+\frac {147\,a^2\,b^5\,c^3\,d^4}{2}+\frac {49\,a\,b^6\,c^4\,d^3}{2}+\frac {21\,b^7\,c^5\,d^2}{10}\right )+a^7\,c^7\,x+\frac {b^7\,d^7\,x^{15}}{15}+\frac {7\,a^4\,c^4\,x^4\,\left (5\,a^3\,d^3+21\,a^2\,b\,c\,d^2+21\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right )}{4}+\frac {7\,b^4\,d^4\,x^{12}\,\left (5\,a^3\,d^3+21\,a^2\,b\,c\,d^2+21\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right )}{12}+\frac {7\,a^6\,c^6\,x^2\,\left (a\,d+b\,c\right )}{2}+\frac {b^6\,d^6\,x^{14}\,\left (a\,d+b\,c\right )}{2}+\frac {7\,a^5\,c^5\,x^3\,\left (3\,a^2\,d^2+7\,a\,b\,c\,d+3\,b^2\,c^2\right )}{3}+\frac {7\,b^5\,d^5\,x^{13}\,\left (3\,a^2\,d^2+7\,a\,b\,c\,d+3\,b^2\,c^2\right )}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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