Optimal. Leaf size=120 \[ -\frac{b^4 \left (a+b \sqrt{x}\right )^{16}}{38760 a^5 x^8}+\frac{2 b^3 \left (a+b \sqrt{x}\right )^{16}}{4845 a^4 x^{17/2}}-\frac{b^2 \left (a+b \sqrt{x}\right )^{16}}{285 a^3 x^9}+\frac{2 b \left (a+b \sqrt{x}\right )^{16}}{95 a^2 x^{19/2}}-\frac{\left (a+b \sqrt{x}\right )^{16}}{10 a x^{10}} \]
[Out]
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Rubi [A] time = 0.138512, antiderivative size = 120, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{b^4 \left (a+b \sqrt{x}\right )^{16}}{38760 a^5 x^8}+\frac{2 b^3 \left (a+b \sqrt{x}\right )^{16}}{4845 a^4 x^{17/2}}-\frac{b^2 \left (a+b \sqrt{x}\right )^{16}}{285 a^3 x^9}+\frac{2 b \left (a+b \sqrt{x}\right )^{16}}{95 a^2 x^{19/2}}-\frac{\left (a+b \sqrt{x}\right )^{16}}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^15/x^11,x]
[Out]
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Rubi in Sympy [A] time = 16.5069, size = 109, normalized size = 0.91 \[ - \frac{\left (a + b \sqrt{x}\right )^{16}}{10 a x^{10}} + \frac{2 b \left (a + b \sqrt{x}\right )^{16}}{95 a^{2} x^{\frac{19}{2}}} - \frac{b^{2} \left (a + b \sqrt{x}\right )^{16}}{285 a^{3} x^{9}} + \frac{2 b^{3} \left (a + b \sqrt{x}\right )^{16}}{4845 a^{4} x^{\frac{17}{2}}} - \frac{b^{4} \left (a + b \sqrt{x}\right )^{16}}{38760 a^{5} x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**15/x**11,x)
[Out]
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Mathematica [A] time = 0.069915, size = 205, normalized size = 1.71 \[ -\frac{a^{15}}{10 x^{10}}-\frac{30 a^{14} b}{19 x^{19/2}}-\frac{35 a^{13} b^2}{3 x^9}-\frac{910 a^{12} b^3}{17 x^{17/2}}-\frac{1365 a^{11} b^4}{8 x^8}-\frac{2002 a^{10} b^5}{5 x^{15/2}}-\frac{715 a^9 b^6}{x^7}-\frac{990 a^8 b^7}{x^{13/2}}-\frac{2145 a^7 b^8}{2 x^6}-\frac{910 a^6 b^9}{x^{11/2}}-\frac{3003 a^5 b^{10}}{5 x^5}-\frac{910 a^4 b^{11}}{3 x^{9/2}}-\frac{455 a^3 b^{12}}{4 x^4}-\frac{30 a^2 b^{13}}{x^{7/2}}-\frac{5 a b^{14}}{x^3}-\frac{2 b^{15}}{5 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^15/x^11,x]
[Out]
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Maple [A] time = 0.005, size = 168, normalized size = 1.4 \[ -{\frac{2\,{b}^{15}}{5}{x}^{-{\frac{5}{2}}}}-5\,{\frac{a{b}^{14}}{{x}^{3}}}-30\,{\frac{{a}^{2}{b}^{13}}{{x}^{7/2}}}-{\frac{455\,{a}^{3}{b}^{12}}{4\,{x}^{4}}}-{\frac{910\,{a}^{4}{b}^{11}}{3}{x}^{-{\frac{9}{2}}}}-{\frac{3003\,{a}^{5}{b}^{10}}{5\,{x}^{5}}}-910\,{\frac{{a}^{6}{b}^{9}}{{x}^{11/2}}}-{\frac{2145\,{a}^{7}{b}^{8}}{2\,{x}^{6}}}-990\,{\frac{{a}^{8}{b}^{7}}{{x}^{13/2}}}-715\,{\frac{{a}^{9}{b}^{6}}{{x}^{7}}}-{\frac{2002\,{a}^{10}{b}^{5}}{5}{x}^{-{\frac{15}{2}}}}-{\frac{1365\,{a}^{11}{b}^{4}}{8\,{x}^{8}}}-{\frac{910\,{a}^{12}{b}^{3}}{17}{x}^{-{\frac{17}{2}}}}-{\frac{35\,{a}^{13}{b}^{2}}{3\,{x}^{9}}}-{\frac{30\,{a}^{14}b}{19}{x}^{-{\frac{19}{2}}}}-{\frac{{a}^{15}}{10\,{x}^{10}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^15/x^11,x)
[Out]
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Maxima [A] time = 1.43838, size = 225, normalized size = 1.88 \[ -\frac{15504 \, b^{15} x^{\frac{15}{2}} + 193800 \, a b^{14} x^{7} + 1162800 \, a^{2} b^{13} x^{\frac{13}{2}} + 4408950 \, a^{3} b^{12} x^{6} + 11757200 \, a^{4} b^{11} x^{\frac{11}{2}} + 23279256 \, a^{5} b^{10} x^{5} + 35271600 \, a^{6} b^{9} x^{\frac{9}{2}} + 41570100 \, a^{7} b^{8} x^{4} + 38372400 \, a^{8} b^{7} x^{\frac{7}{2}} + 27713400 \, a^{9} b^{6} x^{3} + 15519504 \, a^{10} b^{5} x^{\frac{5}{2}} + 6613425 \, a^{11} b^{4} x^{2} + 2074800 \, a^{12} b^{3} x^{\frac{3}{2}} + 452200 \, a^{13} b^{2} x + 61200 \, a^{14} b \sqrt{x} + 3876 \, a^{15}}{38760 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^15/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.240303, size = 227, normalized size = 1.89 \[ -\frac{193800 \, a b^{14} x^{7} + 4408950 \, a^{3} b^{12} x^{6} + 23279256 \, a^{5} b^{10} x^{5} + 41570100 \, a^{7} b^{8} x^{4} + 27713400 \, a^{9} b^{6} x^{3} + 6613425 \, a^{11} b^{4} x^{2} + 452200 \, a^{13} b^{2} x + 3876 \, a^{15} + 16 \,{\left (969 \, b^{15} x^{7} + 72675 \, a^{2} b^{13} x^{6} + 734825 \, a^{4} b^{11} x^{5} + 2204475 \, a^{6} b^{9} x^{4} + 2398275 \, a^{8} b^{7} x^{3} + 969969 \, a^{10} b^{5} x^{2} + 129675 \, a^{12} b^{3} x + 3825 \, a^{14} b\right )} \sqrt{x}}{38760 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^15/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 47.3222, size = 211, normalized size = 1.76 \[ - \frac{a^{15}}{10 x^{10}} - \frac{30 a^{14} b}{19 x^{\frac{19}{2}}} - \frac{35 a^{13} b^{2}}{3 x^{9}} - \frac{910 a^{12} b^{3}}{17 x^{\frac{17}{2}}} - \frac{1365 a^{11} b^{4}}{8 x^{8}} - \frac{2002 a^{10} b^{5}}{5 x^{\frac{15}{2}}} - \frac{715 a^{9} b^{6}}{x^{7}} - \frac{990 a^{8} b^{7}}{x^{\frac{13}{2}}} - \frac{2145 a^{7} b^{8}}{2 x^{6}} - \frac{910 a^{6} b^{9}}{x^{\frac{11}{2}}} - \frac{3003 a^{5} b^{10}}{5 x^{5}} - \frac{910 a^{4} b^{11}}{3 x^{\frac{9}{2}}} - \frac{455 a^{3} b^{12}}{4 x^{4}} - \frac{30 a^{2} b^{13}}{x^{\frac{7}{2}}} - \frac{5 a b^{14}}{x^{3}} - \frac{2 b^{15}}{5 x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**15/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.222945, size = 225, normalized size = 1.88 \[ -\frac{15504 \, b^{15} x^{\frac{15}{2}} + 193800 \, a b^{14} x^{7} + 1162800 \, a^{2} b^{13} x^{\frac{13}{2}} + 4408950 \, a^{3} b^{12} x^{6} + 11757200 \, a^{4} b^{11} x^{\frac{11}{2}} + 23279256 \, a^{5} b^{10} x^{5} + 35271600 \, a^{6} b^{9} x^{\frac{9}{2}} + 41570100 \, a^{7} b^{8} x^{4} + 38372400 \, a^{8} b^{7} x^{\frac{7}{2}} + 27713400 \, a^{9} b^{6} x^{3} + 15519504 \, a^{10} b^{5} x^{\frac{5}{2}} + 6613425 \, a^{11} b^{4} x^{2} + 2074800 \, a^{12} b^{3} x^{\frac{3}{2}} + 452200 \, a^{13} b^{2} x + 61200 \, a^{14} b \sqrt{x} + 3876 \, a^{15}}{38760 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^15/x^11,x, algorithm="giac")
[Out]