Optimal. Leaf size=131 \[ \frac{a^7}{2 b^8 \left (a+b \sqrt{x}\right )^4}-\frac{14 a^6}{3 b^8 \left (a+b \sqrt{x}\right )^3}+\frac{21 a^5}{b^8 \left (a+b \sqrt{x}\right )^2}-\frac{70 a^4}{b^8 \left (a+b \sqrt{x}\right )}-\frac{70 a^3 \log \left (a+b \sqrt{x}\right )}{b^8}+\frac{30 a^2 \sqrt{x}}{b^7}-\frac{5 a x}{b^6}+\frac{2 x^{3/2}}{3 b^5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.229271, antiderivative size = 131, 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 \[ \frac{a^7}{2 b^8 \left (a+b \sqrt{x}\right )^4}-\frac{14 a^6}{3 b^8 \left (a+b \sqrt{x}\right )^3}+\frac{21 a^5}{b^8 \left (a+b \sqrt{x}\right )^2}-\frac{70 a^4}{b^8 \left (a+b \sqrt{x}\right )}-\frac{70 a^3 \log \left (a+b \sqrt{x}\right )}{b^8}+\frac{30 a^2 \sqrt{x}}{b^7}-\frac{5 a x}{b^6}+\frac{2 x^{3/2}}{3 b^5} \]
Antiderivative was successfully verified.
[In] Int[x^3/(a + b*Sqrt[x])^5,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{a^{7}}{2 b^{8} \left (a + b \sqrt{x}\right )^{4}} - \frac{14 a^{6}}{3 b^{8} \left (a + b \sqrt{x}\right )^{3}} + \frac{21 a^{5}}{b^{8} \left (a + b \sqrt{x}\right )^{2}} - \frac{70 a^{4}}{b^{8} \left (a + b \sqrt{x}\right )} - \frac{70 a^{3} \log{\left (a + b \sqrt{x} \right )}}{b^{8}} + \frac{30 a^{2} \sqrt{x}}{b^{7}} - \frac{10 a \int ^{\sqrt{x}} x\, dx}{b^{6}} + \frac{2 x^{\frac{3}{2}}}{3 b^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**3/(a+b*x**(1/2))**5,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0545923, size = 126, normalized size = 0.96 \[ \frac{-319 a^7-856 a^6 b \sqrt{x}-444 a^5 b^2 x+544 a^4 b^3 x^{3/2}+556 a^3 b^4 x^2-420 a^3 \left (a+b \sqrt{x}\right )^4 \log \left (a+b \sqrt{x}\right )+84 a^2 b^5 x^{5/2}-14 a b^6 x^3+4 b^7 x^{7/2}}{6 b^8 \left (a+b \sqrt{x}\right )^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^3/(a + b*Sqrt[x])^5,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 112, normalized size = 0.9 \[ -5\,{\frac{ax}{{b}^{6}}}+{\frac{2}{3\,{b}^{5}}{x}^{{\frac{3}{2}}}}-70\,{\frac{{a}^{3}\ln \left ( a+b\sqrt{x} \right ) }{{b}^{8}}}+30\,{\frac{{a}^{2}\sqrt{x}}{{b}^{7}}}+{\frac{{a}^{7}}{2\,{b}^{8}} \left ( a+b\sqrt{x} \right ) ^{-4}}-{\frac{14\,{a}^{6}}{3\,{b}^{8}} \left ( a+b\sqrt{x} \right ) ^{-3}}+21\,{\frac{{a}^{5}}{{b}^{8} \left ( a+b\sqrt{x} \right ) ^{2}}}-70\,{\frac{{a}^{4}}{{b}^{8} \left ( a+b\sqrt{x} \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^3/(a+b*x^(1/2))^5,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4564, size = 174, normalized size = 1.33 \[ -\frac{70 \, a^{3} \log \left (b \sqrt{x} + a\right )}{b^{8}} + \frac{2 \,{\left (b \sqrt{x} + a\right )}^{3}}{3 \, b^{8}} - \frac{7 \,{\left (b \sqrt{x} + a\right )}^{2} a}{b^{8}} + \frac{42 \,{\left (b \sqrt{x} + a\right )} a^{2}}{b^{8}} - \frac{70 \, a^{4}}{{\left (b \sqrt{x} + a\right )} b^{8}} + \frac{21 \, a^{5}}{{\left (b \sqrt{x} + a\right )}^{2} b^{8}} - \frac{14 \, a^{6}}{3 \,{\left (b \sqrt{x} + a\right )}^{3} b^{8}} + \frac{a^{7}}{2 \,{\left (b \sqrt{x} + a\right )}^{4} b^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*sqrt(x) + a)^5,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.245252, size = 234, normalized size = 1.79 \[ -\frac{14 \, a b^{6} x^{3} - 556 \, a^{3} b^{4} x^{2} + 444 \, a^{5} b^{2} x + 319 \, a^{7} + 420 \,{\left (a^{3} b^{4} x^{2} + 6 \, a^{5} b^{2} x + a^{7} + 4 \,{\left (a^{4} b^{3} x + a^{6} b\right )} \sqrt{x}\right )} \log \left (b \sqrt{x} + a\right ) - 4 \,{\left (b^{7} x^{3} + 21 \, a^{2} b^{5} x^{2} + 136 \, a^{4} b^{3} x - 214 \, a^{6} b\right )} \sqrt{x}}{6 \,{\left (b^{12} x^{2} + 6 \, a^{2} b^{10} x + a^{4} b^{8} + 4 \,{\left (a b^{11} x + a^{3} b^{9}\right )} \sqrt{x}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*sqrt(x) + a)^5,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 10.2422, size = 882, normalized size = 6.73 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**3/(a+b*x**(1/2))**5,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.280281, size = 134, normalized size = 1.02 \[ -\frac{70 \, a^{3}{\rm ln}\left ({\left | b \sqrt{x} + a \right |}\right )}{b^{8}} - \frac{420 \, a^{4} b^{3} x^{\frac{3}{2}} + 1134 \, a^{5} b^{2} x + 1036 \, a^{6} b \sqrt{x} + 319 \, a^{7}}{6 \,{\left (b \sqrt{x} + a\right )}^{4} b^{8}} + \frac{2 \, b^{10} x^{\frac{3}{2}} - 15 \, a b^{9} x + 90 \, a^{2} b^{8} \sqrt{x}}{3 \, b^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^3/(b*sqrt(x) + a)^5,x, algorithm="giac")
[Out]