Optimal. Leaf size=155 \[ \frac{a^9}{2 b^{10} \left (a+b \sqrt{x}\right )^4}-\frac{6 a^8}{b^{10} \left (a+b \sqrt{x}\right )^3}+\frac{36 a^7}{b^{10} \left (a+b \sqrt{x}\right )^2}-\frac{168 a^6}{b^{10} \left (a+b \sqrt{x}\right )}-\frac{252 a^5 \log \left (a+b \sqrt{x}\right )}{b^{10}}+\frac{140 a^4 \sqrt{x}}{b^9}-\frac{35 a^3 x}{b^8}+\frac{10 a^2 x^{3/2}}{b^7}-\frac{5 a x^2}{2 b^6}+\frac{2 x^{5/2}}{5 b^5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.309515, antiderivative size = 155, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{a^9}{2 b^{10} \left (a+b \sqrt{x}\right )^4}-\frac{6 a^8}{b^{10} \left (a+b \sqrt{x}\right )^3}+\frac{36 a^7}{b^{10} \left (a+b \sqrt{x}\right )^2}-\frac{168 a^6}{b^{10} \left (a+b \sqrt{x}\right )}-\frac{252 a^5 \log \left (a+b \sqrt{x}\right )}{b^{10}}+\frac{140 a^4 \sqrt{x}}{b^9}-\frac{35 a^3 x}{b^8}+\frac{10 a^2 x^{3/2}}{b^7}-\frac{5 a x^2}{2 b^6}+\frac{2 x^{5/2}}{5 b^5} \]
Antiderivative was successfully verified.
[In] Int[x^4/(a + b*Sqrt[x])^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{9}}{2 b^{10} \left (a + b \sqrt{x}\right )^{4}} - \frac{6 a^{8}}{b^{10} \left (a + b \sqrt{x}\right )^{3}} + \frac{36 a^{7}}{b^{10} \left (a + b \sqrt{x}\right )^{2}} - \frac{168 a^{6}}{b^{10} \left (a + b \sqrt{x}\right )} - \frac{252 a^{5} \log{\left (a + b \sqrt{x} \right )}}{b^{10}} + \frac{140 a^{4} \sqrt{x}}{b^{9}} - \frac{70 a^{3} \int ^{\sqrt{x}} x\, dx}{b^{8}} + \frac{10 a^{2} x^{\frac{3}{2}}}{b^{7}} - \frac{5 a x^{2}}{2 b^{6}} + \frac{2 x^{\frac{5}{2}}}{5 b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(a+b*x**(1/2))**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.064673, size = 150, normalized size = 0.97 \[ \frac{-1375 a^9-2980 a^8 b \sqrt{x}+570 a^7 b^2 x+5420 a^6 b^3 x^{3/2}+3875 a^5 b^4 x^2-2520 a^5 \left (a+b \sqrt{x}\right )^4 \log \left (a+b \sqrt{x}\right )+504 a^4 b^5 x^{5/2}-84 a^3 b^6 x^3+24 a^2 b^7 x^{7/2}-9 a b^8 x^4+4 b^9 x^{9/2}}{10 b^{10} \left (a+b \sqrt{x}\right )^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(a + b*Sqrt[x])^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.015, size = 134, normalized size = 0.9 \[ -35\,{\frac{{a}^{3}x}{{b}^{8}}}+10\,{\frac{{a}^{2}{x}^{3/2}}{{b}^{7}}}-{\frac{5\,a{x}^{2}}{2\,{b}^{6}}}+{\frac{2}{5\,{b}^{5}}{x}^{{\frac{5}{2}}}}-252\,{\frac{{a}^{5}\ln \left ( a+b\sqrt{x} \right ) }{{b}^{10}}}+140\,{\frac{{a}^{4}\sqrt{x}}{{b}^{9}}}+{\frac{{a}^{9}}{2\,{b}^{10}} \left ( a+b\sqrt{x} \right ) ^{-4}}-6\,{\frac{{a}^{8}}{{b}^{10} \left ( a+b\sqrt{x} \right ) ^{3}}}+36\,{\frac{{a}^{7}}{{b}^{10} \left ( a+b\sqrt{x} \right ) ^{2}}}-168\,{\frac{{a}^{6}}{{b}^{10} \left ( a+b\sqrt{x} \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(a+b*x^(1/2))^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42974, size = 220, normalized size = 1.42 \[ -\frac{252 \, a^{5} \log \left (b \sqrt{x} + a\right )}{b^{10}} + \frac{2 \,{\left (b \sqrt{x} + a\right )}^{5}}{5 \, b^{10}} - \frac{9 \,{\left (b \sqrt{x} + a\right )}^{4} a}{2 \, b^{10}} + \frac{24 \,{\left (b \sqrt{x} + a\right )}^{3} a^{2}}{b^{10}} - \frac{84 \,{\left (b \sqrt{x} + a\right )}^{2} a^{3}}{b^{10}} + \frac{252 \,{\left (b \sqrt{x} + a\right )} a^{4}}{b^{10}} - \frac{168 \, a^{6}}{{\left (b \sqrt{x} + a\right )} b^{10}} + \frac{36 \, a^{7}}{{\left (b \sqrt{x} + a\right )}^{2} b^{10}} - \frac{6 \, a^{8}}{{\left (b \sqrt{x} + a\right )}^{3} b^{10}} + \frac{a^{9}}{2 \,{\left (b \sqrt{x} + a\right )}^{4} b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*sqrt(x) + a)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.246303, size = 263, normalized size = 1.7 \[ -\frac{9 \, a b^{8} x^{4} + 84 \, a^{3} b^{6} x^{3} - 3875 \, a^{5} b^{4} x^{2} - 570 \, a^{7} b^{2} x + 1375 \, a^{9} + 2520 \,{\left (a^{5} b^{4} x^{2} + 6 \, a^{7} b^{2} x + a^{9} + 4 \,{\left (a^{6} b^{3} x + a^{8} b\right )} \sqrt{x}\right )} \log \left (b \sqrt{x} + a\right ) - 4 \,{\left (b^{9} x^{4} + 6 \, a^{2} b^{7} x^{3} + 126 \, a^{4} b^{5} x^{2} + 1355 \, a^{6} b^{3} x - 745 \, a^{8} b\right )} \sqrt{x}}{10 \,{\left (b^{14} x^{2} + 6 \, a^{2} b^{12} x + a^{4} b^{10} + 4 \,{\left (a b^{13} x + a^{3} b^{11}\right )} \sqrt{x}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*sqrt(x) + a)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 26.4734, size = 1013, normalized size = 6.54 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(a+b*x**(1/2))**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.259332, size = 163, normalized size = 1.05 \[ -\frac{252 \, a^{5}{\rm ln}\left ({\left | b \sqrt{x} + a \right |}\right )}{b^{10}} - \frac{336 \, a^{6} b^{3} x^{\frac{3}{2}} + 936 \, a^{7} b^{2} x + 876 \, a^{8} b \sqrt{x} + 275 \, a^{9}}{2 \,{\left (b \sqrt{x} + a\right )}^{4} b^{10}} + \frac{4 \, b^{20} x^{\frac{5}{2}} - 25 \, a b^{19} x^{2} + 100 \, a^{2} b^{18} x^{\frac{3}{2}} - 350 \, a^{3} b^{17} x + 1400 \, a^{4} b^{16} \sqrt{x}}{10 \, b^{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*sqrt(x) + a)^5,x, algorithm="giac")
[Out]