Optimal. Leaf size=207 \[ -\frac {a^{15}}{16 x^{16}}-\frac {30 a^{14} b}{31 x^{31/2}}-\frac {7 a^{13} b^2}{x^{15}}-\frac {910 a^{12} b^3}{29 x^{29/2}}-\frac {195 a^{11} b^4}{2 x^{14}}-\frac {2002 a^{10} b^5}{9 x^{27/2}}-\frac {385 a^9 b^6}{x^{13}}-\frac {2574 a^8 b^7}{5 x^{25/2}}-\frac {2145 a^7 b^8}{4 x^{12}}-\frac {10010 a^6 b^9}{23 x^{23/2}}-\frac {273 a^5 b^{10}}{x^{11}}-\frac {130 a^4 b^{11}}{x^{21/2}}-\frac {91 a^3 b^{12}}{2 x^{10}}-\frac {210 a^2 b^{13}}{19 x^{19/2}}-\frac {5 a b^{14}}{3 x^9}-\frac {2 b^{15}}{17 x^{17/2}} \]
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Rubi [A] time = 0.11, antiderivative size = 207, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac {7 a^{13} b^2}{x^{15}}-\frac {910 a^{12} b^3}{29 x^{29/2}}-\frac {195 a^{11} b^4}{2 x^{14}}-\frac {2002 a^{10} b^5}{9 x^{27/2}}-\frac {385 a^9 b^6}{x^{13}}-\frac {2574 a^8 b^7}{5 x^{25/2}}-\frac {2145 a^7 b^8}{4 x^{12}}-\frac {10010 a^6 b^9}{23 x^{23/2}}-\frac {273 a^5 b^{10}}{x^{11}}-\frac {130 a^4 b^{11}}{x^{21/2}}-\frac {91 a^3 b^{12}}{2 x^{10}}-\frac {210 a^2 b^{13}}{19 x^{19/2}}-\frac {30 a^{14} b}{31 x^{31/2}}-\frac {a^{15}}{16 x^{16}}-\frac {5 a b^{14}}{3 x^9}-\frac {2 b^{15}}{17 x^{17/2}} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{17}} \, dx &=2 \operatorname {Subst}\left (\int \frac {(a+b x)^{15}}{x^{33}} \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (\frac {a^{15}}{x^{33}}+\frac {15 a^{14} b}{x^{32}}+\frac {105 a^{13} b^2}{x^{31}}+\frac {455 a^{12} b^3}{x^{30}}+\frac {1365 a^{11} b^4}{x^{29}}+\frac {3003 a^{10} b^5}{x^{28}}+\frac {5005 a^9 b^6}{x^{27}}+\frac {6435 a^8 b^7}{x^{26}}+\frac {6435 a^7 b^8}{x^{25}}+\frac {5005 a^6 b^9}{x^{24}}+\frac {3003 a^5 b^{10}}{x^{23}}+\frac {1365 a^4 b^{11}}{x^{22}}+\frac {455 a^3 b^{12}}{x^{21}}+\frac {105 a^2 b^{13}}{x^{20}}+\frac {15 a b^{14}}{x^{19}}+\frac {b^{15}}{x^{18}}\right ) \, dx,x,\sqrt {x}\right )\\ &=-\frac {a^{15}}{16 x^{16}}-\frac {30 a^{14} b}{31 x^{31/2}}-\frac {7 a^{13} b^2}{x^{15}}-\frac {910 a^{12} b^3}{29 x^{29/2}}-\frac {195 a^{11} b^4}{2 x^{14}}-\frac {2002 a^{10} b^5}{9 x^{27/2}}-\frac {385 a^9 b^6}{x^{13}}-\frac {2574 a^8 b^7}{5 x^{25/2}}-\frac {2145 a^7 b^8}{4 x^{12}}-\frac {10010 a^6 b^9}{23 x^{23/2}}-\frac {273 a^5 b^{10}}{x^{11}}-\frac {130 a^4 b^{11}}{x^{21/2}}-\frac {91 a^3 b^{12}}{2 x^{10}}-\frac {210 a^2 b^{13}}{19 x^{19/2}}-\frac {5 a b^{14}}{3 x^9}-\frac {2 b^{15}}{17 x^{17/2}}\\ \end {align*}
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Mathematica [A] time = 0.14, size = 207, normalized size = 1.00 \[ -\frac {a^{15}}{16 x^{16}}-\frac {30 a^{14} b}{31 x^{31/2}}-\frac {7 a^{13} b^2}{x^{15}}-\frac {910 a^{12} b^3}{29 x^{29/2}}-\frac {195 a^{11} b^4}{2 x^{14}}-\frac {2002 a^{10} b^5}{9 x^{27/2}}-\frac {385 a^9 b^6}{x^{13}}-\frac {2574 a^8 b^7}{5 x^{25/2}}-\frac {2145 a^7 b^8}{4 x^{12}}-\frac {10010 a^6 b^9}{23 x^{23/2}}-\frac {273 a^5 b^{10}}{x^{11}}-\frac {130 a^4 b^{11}}{x^{21/2}}-\frac {91 a^3 b^{12}}{2 x^{10}}-\frac {210 a^2 b^{13}}{19 x^{19/2}}-\frac {5 a b^{14}}{3 x^9}-\frac {2 b^{15}}{17 x^{17/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 168, normalized size = 0.81 \[ -\frac {8014405200 \, a b^{14} x^{7} + 218793261960 \, a^{3} b^{12} x^{6} + 1312759571760 \, a^{5} b^{10} x^{5} + 2578634873100 \, a^{7} b^{8} x^{4} + 1851327601200 \, a^{9} b^{6} x^{3} + 468842704200 \, a^{11} b^{4} x^{2} + 33660501840 \, a^{13} b^{2} x + 300540195 \, a^{15} + 32 \, {\left (17678835 \, b^{15} x^{7} + 1660880025 \, a^{2} b^{13} x^{6} + 19535112675 \, a^{4} b^{11} x^{5} + 65400159825 \, a^{6} b^{9} x^{4} + 77359046193 \, a^{8} b^{7} x^{3} + 33426748355 \, a^{10} b^{5} x^{2} + 4715372025 \, a^{12} b^{3} x + 145422675 \, a^{14} b\right )} \sqrt {x}}{4808643120 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 167, normalized size = 0.81 \[ -\frac {565722720 \, b^{15} x^{\frac {15}{2}} + 8014405200 \, a b^{14} x^{7} + 53148160800 \, a^{2} b^{13} x^{\frac {13}{2}} + 218793261960 \, a^{3} b^{12} x^{6} + 625123605600 \, a^{4} b^{11} x^{\frac {11}{2}} + 1312759571760 \, a^{5} b^{10} x^{5} + 2092805114400 \, a^{6} b^{9} x^{\frac {9}{2}} + 2578634873100 \, a^{7} b^{8} x^{4} + 2475489478176 \, a^{8} b^{7} x^{\frac {7}{2}} + 1851327601200 \, a^{9} b^{6} x^{3} + 1069655947360 \, a^{10} b^{5} x^{\frac {5}{2}} + 468842704200 \, a^{11} b^{4} x^{2} + 150891904800 \, a^{12} b^{3} x^{\frac {3}{2}} + 33660501840 \, a^{13} b^{2} x + 4653525600 \, a^{14} b \sqrt {x} + 300540195 \, a^{15}}{4808643120 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 168, normalized size = 0.81 \[ -\frac {2 b^{15}}{17 x^{\frac {17}{2}}}-\frac {5 a \,b^{14}}{3 x^{9}}-\frac {210 a^{2} b^{13}}{19 x^{\frac {19}{2}}}-\frac {91 a^{3} b^{12}}{2 x^{10}}-\frac {130 a^{4} b^{11}}{x^{\frac {21}{2}}}-\frac {273 a^{5} b^{10}}{x^{11}}-\frac {10010 a^{6} b^{9}}{23 x^{\frac {23}{2}}}-\frac {2145 a^{7} b^{8}}{4 x^{12}}-\frac {2574 a^{8} b^{7}}{5 x^{\frac {25}{2}}}-\frac {385 a^{9} b^{6}}{x^{13}}-\frac {2002 a^{10} b^{5}}{9 x^{\frac {27}{2}}}-\frac {195 a^{11} b^{4}}{2 x^{14}}-\frac {910 a^{12} b^{3}}{29 x^{\frac {29}{2}}}-\frac {7 a^{13} b^{2}}{x^{15}}-\frac {30 a^{14} b}{31 x^{\frac {31}{2}}}-\frac {a^{15}}{16 x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.87, size = 167, normalized size = 0.81 \[ -\frac {565722720 \, b^{15} x^{\frac {15}{2}} + 8014405200 \, a b^{14} x^{7} + 53148160800 \, a^{2} b^{13} x^{\frac {13}{2}} + 218793261960 \, a^{3} b^{12} x^{6} + 625123605600 \, a^{4} b^{11} x^{\frac {11}{2}} + 1312759571760 \, a^{5} b^{10} x^{5} + 2092805114400 \, a^{6} b^{9} x^{\frac {9}{2}} + 2578634873100 \, a^{7} b^{8} x^{4} + 2475489478176 \, a^{8} b^{7} x^{\frac {7}{2}} + 1851327601200 \, a^{9} b^{6} x^{3} + 1069655947360 \, a^{10} b^{5} x^{\frac {5}{2}} + 468842704200 \, a^{11} b^{4} x^{2} + 150891904800 \, a^{12} b^{3} x^{\frac {3}{2}} + 33660501840 \, a^{13} b^{2} x + 4653525600 \, a^{14} b \sqrt {x} + 300540195 \, a^{15}}{4808643120 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 167, normalized size = 0.81 \[ -\frac {\frac {a^{15}}{16}+\frac {2\,b^{15}\,x^{15/2}}{17}+7\,a^{13}\,b^2\,x+\frac {30\,a^{14}\,b\,\sqrt {x}}{31}+\frac {5\,a\,b^{14}\,x^7}{3}+\frac {195\,a^{11}\,b^4\,x^2}{2}+385\,a^9\,b^6\,x^3+\frac {2145\,a^7\,b^8\,x^4}{4}+273\,a^5\,b^{10}\,x^5+\frac {910\,a^{12}\,b^3\,x^{3/2}}{29}+\frac {91\,a^3\,b^{12}\,x^6}{2}+\frac {2002\,a^{10}\,b^5\,x^{5/2}}{9}+\frac {2574\,a^8\,b^7\,x^{7/2}}{5}+\frac {10010\,a^6\,b^9\,x^{9/2}}{23}+130\,a^4\,b^{11}\,x^{11/2}+\frac {210\,a^2\,b^{13}\,x^{13/2}}{19}}{x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 51.04, size = 212, normalized size = 1.02 \[ - \frac {a^{15}}{16 x^{16}} - \frac {30 a^{14} b}{31 x^{\frac {31}{2}}} - \frac {7 a^{13} b^{2}}{x^{15}} - \frac {910 a^{12} b^{3}}{29 x^{\frac {29}{2}}} - \frac {195 a^{11} b^{4}}{2 x^{14}} - \frac {2002 a^{10} b^{5}}{9 x^{\frac {27}{2}}} - \frac {385 a^{9} b^{6}}{x^{13}} - \frac {2574 a^{8} b^{7}}{5 x^{\frac {25}{2}}} - \frac {2145 a^{7} b^{8}}{4 x^{12}} - \frac {10010 a^{6} b^{9}}{23 x^{\frac {23}{2}}} - \frac {273 a^{5} b^{10}}{x^{11}} - \frac {130 a^{4} b^{11}}{x^{\frac {21}{2}}} - \frac {91 a^{3} b^{12}}{2 x^{10}} - \frac {210 a^{2} b^{13}}{19 x^{\frac {19}{2}}} - \frac {5 a b^{14}}{3 x^{9}} - \frac {2 b^{15}}{17 x^{\frac {17}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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