Optimal. Leaf size=125 \[ -\frac{a^{10}}{x}-\frac{15 a^9 b}{x^{2/3}}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.177705, antiderivative size = 125, 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 \[ -\frac{a^{10}}{x}-\frac{15 a^9 b}{x^{2/3}}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^(1/3))^10/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{10}}{x} - \frac{15 a^{9} b}{x^{\frac{2}{3}}} - \frac{135 a^{8} b^{2}}{\sqrt [3]{x}} + 360 a^{7} b^{3} \log{\left (\sqrt [3]{x} \right )} + 630 a^{6} b^{4} \sqrt [3]{x} + 756 a^{5} b^{5} \int ^{\sqrt [3]{x}} x\, dx + 210 a^{4} b^{6} x + 90 a^{3} b^{7} x^{\frac{4}{3}} + 27 a^{2} b^{8} x^{\frac{5}{3}} + 5 a b^{9} x^{2} + \frac{3 b^{10} x^{\frac{7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/3))**10/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0784842, size = 125, normalized size = 1. \[ -\frac{a^{10}}{x}-\frac{15 a^9 b}{x^{2/3}}-\frac{135 a^8 b^2}{\sqrt [3]{x}}+120 a^7 b^3 \log (x)+630 a^6 b^4 \sqrt [3]{x}+378 a^5 b^5 x^{2/3}+210 a^4 b^6 x+90 a^3 b^7 x^{4/3}+27 a^2 b^8 x^{5/3}+5 a b^9 x^2+\frac{3}{7} b^{10} x^{7/3} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^(1/3))^10/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 110, normalized size = 0.9 \[ -{\frac{{a}^{10}}{x}}-15\,{\frac{{a}^{9}b}{{x}^{2/3}}}-135\,{\frac{{a}^{8}{b}^{2}}{\sqrt [3]{x}}}+630\,{a}^{6}{b}^{4}\sqrt [3]{x}+378\,{a}^{5}{b}^{5}{x}^{2/3}+210\,{a}^{4}{b}^{6}x+90\,{a}^{3}{b}^{7}{x}^{4/3}+27\,{a}^{2}{b}^{8}{x}^{5/3}+5\,a{b}^{9}{x}^{2}+{\frac{3\,{b}^{10}}{7}{x}^{{\frac{7}{3}}}}+120\,{a}^{7}{b}^{3}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/3))^10/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44521, size = 149, normalized size = 1.19 \[ \frac{3}{7} \, b^{10} x^{\frac{7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac{5}{3}} + 90 \, a^{3} b^{7} x^{\frac{4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3} \log \left (x\right ) + 378 \, a^{5} b^{5} x^{\frac{2}{3}} + 630 \, a^{6} b^{4} x^{\frac{1}{3}} - \frac{135 \, a^{8} b^{2} x^{\frac{2}{3}} + 15 \, a^{9} b x^{\frac{1}{3}} + a^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^10/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228604, size = 157, normalized size = 1.26 \[ \frac{35 \, a b^{9} x^{3} + 1470 \, a^{4} b^{6} x^{2} + 2520 \, a^{7} b^{3} x \log \left (x^{\frac{1}{3}}\right ) - 7 \, a^{10} + 189 \,{\left (a^{2} b^{8} x^{2} + 14 \, a^{5} b^{5} x - 5 \, a^{8} b^{2}\right )} x^{\frac{2}{3}} + 3 \,{\left (b^{10} x^{3} + 210 \, a^{3} b^{7} x^{2} + 1470 \, a^{6} b^{4} x - 35 \, a^{9} b\right )} x^{\frac{1}{3}}}{7 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^10/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 10.0192, size = 128, normalized size = 1.02 \[ - \frac{a^{10}}{x} - \frac{15 a^{9} b}{x^{\frac{2}{3}}} - \frac{135 a^{8} b^{2}}{\sqrt [3]{x}} + 120 a^{7} b^{3} \log{\left (x \right )} + 630 a^{6} b^{4} \sqrt [3]{x} + 378 a^{5} b^{5} x^{\frac{2}{3}} + 210 a^{4} b^{6} x + 90 a^{3} b^{7} x^{\frac{4}{3}} + 27 a^{2} b^{8} x^{\frac{5}{3}} + 5 a b^{9} x^{2} + \frac{3 b^{10} x^{\frac{7}{3}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/3))**10/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.256255, size = 150, normalized size = 1.2 \[ \frac{3}{7} \, b^{10} x^{\frac{7}{3}} + 5 \, a b^{9} x^{2} + 27 \, a^{2} b^{8} x^{\frac{5}{3}} + 90 \, a^{3} b^{7} x^{\frac{4}{3}} + 210 \, a^{4} b^{6} x + 120 \, a^{7} b^{3}{\rm ln}\left ({\left | x \right |}\right ) + 378 \, a^{5} b^{5} x^{\frac{2}{3}} + 630 \, a^{6} b^{4} x^{\frac{1}{3}} - \frac{135 \, a^{8} b^{2} x^{\frac{2}{3}} + 15 \, a^{9} b x^{\frac{1}{3}} + a^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(1/3) + a)^10/x^2,x, algorithm="giac")
[Out]