Optimal. Leaf size=229 \[ -\frac {a^{10} A}{20 x^{20}}-\frac {a^9 (10 A b+a B)}{19 x^{19}}-\frac {5 a^8 b (9 A b+2 a B)}{18 x^{18}}-\frac {15 a^7 b^2 (8 A b+3 a B)}{17 x^{17}}-\frac {15 a^6 b^3 (7 A b+4 a B)}{8 x^{16}}-\frac {14 a^5 b^4 (6 A b+5 a B)}{5 x^{15}}-\frac {3 a^4 b^5 (5 A b+6 a B)}{x^{14}}-\frac {30 a^3 b^6 (4 A b+7 a B)}{13 x^{13}}-\frac {5 a^2 b^7 (3 A b+8 a B)}{4 x^{12}}-\frac {5 a b^8 (2 A b+9 a B)}{11 x^{11}}-\frac {b^9 (A b+10 a B)}{10 x^{10}}-\frac {b^{10} B}{9 x^9} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.09, antiderivative size = 229, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {77}
\begin {gather*} -\frac {a^{10} A}{20 x^{20}}-\frac {a^9 (a B+10 A b)}{19 x^{19}}-\frac {5 a^8 b (2 a B+9 A b)}{18 x^{18}}-\frac {15 a^7 b^2 (3 a B+8 A b)}{17 x^{17}}-\frac {15 a^6 b^3 (4 a B+7 A b)}{8 x^{16}}-\frac {14 a^5 b^4 (5 a B+6 A b)}{5 x^{15}}-\frac {3 a^4 b^5 (6 a B+5 A b)}{x^{14}}-\frac {30 a^3 b^6 (7 a B+4 A b)}{13 x^{13}}-\frac {5 a^2 b^7 (8 a B+3 A b)}{4 x^{12}}-\frac {b^9 (10 a B+A b)}{10 x^{10}}-\frac {5 a b^8 (9 a B+2 A b)}{11 x^{11}}-\frac {b^{10} B}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(a+b x)^{10} (A+B x)}{x^{21}} \, dx &=\int \left (\frac {a^{10} A}{x^{21}}+\frac {a^9 (10 A b+a B)}{x^{20}}+\frac {5 a^8 b (9 A b+2 a B)}{x^{19}}+\frac {15 a^7 b^2 (8 A b+3 a B)}{x^{18}}+\frac {30 a^6 b^3 (7 A b+4 a B)}{x^{17}}+\frac {42 a^5 b^4 (6 A b+5 a B)}{x^{16}}+\frac {42 a^4 b^5 (5 A b+6 a B)}{x^{15}}+\frac {30 a^3 b^6 (4 A b+7 a B)}{x^{14}}+\frac {15 a^2 b^7 (3 A b+8 a B)}{x^{13}}+\frac {5 a b^8 (2 A b+9 a B)}{x^{12}}+\frac {b^9 (A b+10 a B)}{x^{11}}+\frac {b^{10} B}{x^{10}}\right ) \, dx\\ &=-\frac {a^{10} A}{20 x^{20}}-\frac {a^9 (10 A b+a B)}{19 x^{19}}-\frac {5 a^8 b (9 A b+2 a B)}{18 x^{18}}-\frac {15 a^7 b^2 (8 A b+3 a B)}{17 x^{17}}-\frac {15 a^6 b^3 (7 A b+4 a B)}{8 x^{16}}-\frac {14 a^5 b^4 (6 A b+5 a B)}{5 x^{15}}-\frac {3 a^4 b^5 (5 A b+6 a B)}{x^{14}}-\frac {30 a^3 b^6 (4 A b+7 a B)}{13 x^{13}}-\frac {5 a^2 b^7 (3 A b+8 a B)}{4 x^{12}}-\frac {5 a b^8 (2 A b+9 a B)}{11 x^{11}}-\frac {b^9 (A b+10 a B)}{10 x^{10}}-\frac {b^{10} B}{9 x^9}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 222, normalized size = 0.97 \begin {gather*} -\frac {b^{10} (9 A+10 B x)}{90 x^{10}}-\frac {a b^9 (10 A+11 B x)}{11 x^{11}}-\frac {15 a^2 b^8 (11 A+12 B x)}{44 x^{12}}-\frac {10 a^3 b^7 (12 A+13 B x)}{13 x^{13}}-\frac {15 a^4 b^6 (13 A+14 B x)}{13 x^{14}}-\frac {6 a^5 b^5 (14 A+15 B x)}{5 x^{15}}-\frac {7 a^6 b^4 (15 A+16 B x)}{8 x^{16}}-\frac {15 a^7 b^3 (16 A+17 B x)}{34 x^{17}}-\frac {5 a^8 b^2 (17 A+18 B x)}{34 x^{18}}-\frac {5 a^9 b (18 A+19 B x)}{171 x^{19}}-\frac {a^{10} (19 A+20 B x)}{380 x^{20}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 208, normalized size = 0.91
method | result | size |
default | \(-\frac {a^{10} A}{20 x^{20}}-\frac {a^{9} \left (10 A b +B a \right )}{19 x^{19}}-\frac {5 a^{8} b \left (9 A b +2 B a \right )}{18 x^{18}}-\frac {15 a^{7} b^{2} \left (8 A b +3 B a \right )}{17 x^{17}}-\frac {15 a^{6} b^{3} \left (7 A b +4 B a \right )}{8 x^{16}}-\frac {14 a^{5} b^{4} \left (6 A b +5 B a \right )}{5 x^{15}}-\frac {3 a^{4} b^{5} \left (5 A b +6 B a \right )}{x^{14}}-\frac {30 a^{3} b^{6} \left (4 A b +7 B a \right )}{13 x^{13}}-\frac {5 a^{2} b^{7} \left (3 A b +8 B a \right )}{4 x^{12}}-\frac {5 a \,b^{8} \left (2 A b +9 B a \right )}{11 x^{11}}-\frac {b^{9} \left (A b +10 B a \right )}{10 x^{10}}-\frac {b^{10} B}{9 x^{9}}\) | \(208\) |
norman | \(\frac {-\frac {a^{10} A}{20}+\left (-\frac {10}{19} a^{9} b A -\frac {1}{19} a^{10} B \right ) x +\left (-\frac {5}{2} a^{8} b^{2} A -\frac {5}{9} a^{9} b B \right ) x^{2}+\left (-\frac {120}{17} a^{7} b^{3} A -\frac {45}{17} a^{8} b^{2} B \right ) x^{3}+\left (-\frac {105}{8} a^{6} b^{4} A -\frac {15}{2} a^{7} b^{3} B \right ) x^{4}+\left (-\frac {84}{5} a^{5} b^{5} A -14 a^{6} b^{4} B \right ) x^{5}+\left (-15 a^{4} b^{6} A -18 a^{5} b^{5} B \right ) x^{6}+\left (-\frac {120}{13} a^{3} b^{7} A -\frac {210}{13} a^{4} b^{6} B \right ) x^{7}+\left (-\frac {15}{4} a^{2} b^{8} A -10 a^{3} b^{7} B \right ) x^{8}+\left (-\frac {10}{11} a \,b^{9} A -\frac {45}{11} a^{2} b^{8} B \right ) x^{9}+\left (-\frac {1}{10} b^{10} A -a \,b^{9} B \right ) x^{10}-\frac {b^{10} B \,x^{11}}{9}}{x^{20}}\) | \(235\) |
risch | \(\frac {-\frac {a^{10} A}{20}+\left (-\frac {10}{19} a^{9} b A -\frac {1}{19} a^{10} B \right ) x +\left (-\frac {5}{2} a^{8} b^{2} A -\frac {5}{9} a^{9} b B \right ) x^{2}+\left (-\frac {120}{17} a^{7} b^{3} A -\frac {45}{17} a^{8} b^{2} B \right ) x^{3}+\left (-\frac {105}{8} a^{6} b^{4} A -\frac {15}{2} a^{7} b^{3} B \right ) x^{4}+\left (-\frac {84}{5} a^{5} b^{5} A -14 a^{6} b^{4} B \right ) x^{5}+\left (-15 a^{4} b^{6} A -18 a^{5} b^{5} B \right ) x^{6}+\left (-\frac {120}{13} a^{3} b^{7} A -\frac {210}{13} a^{4} b^{6} B \right ) x^{7}+\left (-\frac {15}{4} a^{2} b^{8} A -10 a^{3} b^{7} B \right ) x^{8}+\left (-\frac {10}{11} a \,b^{9} A -\frac {45}{11} a^{2} b^{8} B \right ) x^{9}+\left (-\frac {1}{10} b^{10} A -a \,b^{9} B \right ) x^{10}-\frac {b^{10} B \,x^{11}}{9}}{x^{20}}\) | \(235\) |
gosper | \(-\frac {1847560 b^{10} B \,x^{11}+1662804 A \,b^{10} x^{10}+16628040 B a \,b^{9} x^{10}+15116400 a A \,b^{9} x^{9}+68023800 B \,a^{2} b^{8} x^{9}+62355150 a^{2} A \,b^{8} x^{8}+166280400 B \,a^{3} b^{7} x^{8}+153489600 a^{3} A \,b^{7} x^{7}+268606800 B \,a^{4} b^{6} x^{7}+249420600 a^{4} A \,b^{6} x^{6}+299304720 B \,a^{5} b^{5} x^{6}+279351072 a^{5} A \,b^{5} x^{5}+232792560 B \,a^{6} b^{4} x^{5}+218243025 a^{6} A \,b^{4} x^{4}+124710300 B \,a^{7} b^{3} x^{4}+117374400 a^{7} A \,b^{3} x^{3}+44015400 B \,a^{8} b^{2} x^{3}+41570100 a^{8} A \,b^{2} x^{2}+9237800 B \,a^{9} b \,x^{2}+8751600 a^{9} A b x +875160 a^{10} B x +831402 a^{10} A}{16628040 x^{20}}\) | \(244\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 243, normalized size = 1.06 \begin {gather*} -\frac {1847560 \, B b^{10} x^{11} + 831402 \, A a^{10} + 1662804 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 7558200 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 20785050 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 38372400 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 49884120 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 46558512 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 31177575 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 14671800 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 4618900 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 875160 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x}{16628040 \, x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.36, size = 243, normalized size = 1.06 \begin {gather*} -\frac {1847560 \, B b^{10} x^{11} + 831402 \, A a^{10} + 1662804 \, {\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 7558200 \, {\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 20785050 \, {\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 38372400 \, {\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 49884120 \, {\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 46558512 \, {\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} + 31177575 \, {\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 14671800 \, {\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 4618900 \, {\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 875160 \, {\left (B a^{10} + 10 \, A a^{9} b\right )} x}{16628040 \, x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.99, size = 243, normalized size = 1.06 \begin {gather*} -\frac {1847560 \, B b^{10} x^{11} + 16628040 \, B a b^{9} x^{10} + 1662804 \, A b^{10} x^{10} + 68023800 \, B a^{2} b^{8} x^{9} + 15116400 \, A a b^{9} x^{9} + 166280400 \, B a^{3} b^{7} x^{8} + 62355150 \, A a^{2} b^{8} x^{8} + 268606800 \, B a^{4} b^{6} x^{7} + 153489600 \, A a^{3} b^{7} x^{7} + 299304720 \, B a^{5} b^{5} x^{6} + 249420600 \, A a^{4} b^{6} x^{6} + 232792560 \, B a^{6} b^{4} x^{5} + 279351072 \, A a^{5} b^{5} x^{5} + 124710300 \, B a^{7} b^{3} x^{4} + 218243025 \, A a^{6} b^{4} x^{4} + 44015400 \, B a^{8} b^{2} x^{3} + 117374400 \, A a^{7} b^{3} x^{3} + 9237800 \, B a^{9} b x^{2} + 41570100 \, A a^{8} b^{2} x^{2} + 875160 \, B a^{10} x + 8751600 \, A a^{9} b x + 831402 \, A a^{10}}{16628040 \, x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.13, size = 234, normalized size = 1.02 \begin {gather*} -\frac {x\,\left (\frac {B\,a^{10}}{19}+\frac {10\,A\,b\,a^9}{19}\right )+\frac {A\,a^{10}}{20}+x^2\,\left (\frac {5\,B\,a^9\,b}{9}+\frac {5\,A\,a^8\,b^2}{2}\right )+x^9\,\left (\frac {45\,B\,a^2\,b^8}{11}+\frac {10\,A\,a\,b^9}{11}\right )+x^{10}\,\left (\frac {A\,b^{10}}{10}+B\,a\,b^9\right )+x^8\,\left (10\,B\,a^3\,b^7+\frac {15\,A\,a^2\,b^8}{4}\right )+x^6\,\left (18\,B\,a^5\,b^5+15\,A\,a^4\,b^6\right )+x^5\,\left (14\,B\,a^6\,b^4+\frac {84\,A\,a^5\,b^5}{5}\right )+x^4\,\left (\frac {15\,B\,a^7\,b^3}{2}+\frac {105\,A\,a^6\,b^4}{8}\right )+x^3\,\left (\frac {45\,B\,a^8\,b^2}{17}+\frac {120\,A\,a^7\,b^3}{17}\right )+x^7\,\left (\frac {210\,B\,a^4\,b^6}{13}+\frac {120\,A\,a^3\,b^7}{13}\right )+\frac {B\,b^{10}\,x^{11}}{9}}{x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________