Optimal. Leaf size=46 \[ \frac{b \left (a+b \sqrt{x}\right )^{11}}{66 a^2 x^{11/2}}-\frac{\left (a+b \sqrt{x}\right )^{11}}{6 a x^6} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0517067, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{b \left (a+b \sqrt{x}\right )^{11}}{66 a^2 x^{11/2}}-\frac{\left (a+b \sqrt{x}\right )^{11}}{6 a x^6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^10/x^7,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.77653, size = 37, normalized size = 0.8 \[ - \frac{\left (a + b \sqrt{x}\right )^{11}}{6 a x^{6}} + \frac{b \left (a + b \sqrt{x}\right )^{11}}{66 a^{2} x^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**10/x**7,x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.0357603, size = 124, normalized size = 2.7 \[ -\frac{11 a^{10}+120 a^9 b \sqrt{x}+594 a^8 b^2 x+1760 a^7 b^3 x^{3/2}+3465 a^6 b^4 x^2+4752 a^5 b^5 x^{5/2}+4620 a^4 b^6 x^3+3168 a^3 b^7 x^{7/2}+1485 a^2 b^8 x^4+440 a b^9 x^{9/2}+66 b^{10} x^5}{66 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^10/x^7,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.004, size = 113, normalized size = 2.5 \[ -{\frac{{b}^{10}}{x}}-{\frac{20\,a{b}^{9}}{3}{x}^{-{\frac{3}{2}}}}-{\frac{45\,{a}^{2}{b}^{8}}{2\,{x}^{2}}}-48\,{\frac{{a}^{3}{b}^{7}}{{x}^{5/2}}}-70\,{\frac{{a}^{4}{b}^{6}}{{x}^{3}}}-72\,{\frac{{a}^{5}{b}^{5}}{{x}^{7/2}}}-{\frac{105\,{a}^{6}{b}^{4}}{2\,{x}^{4}}}-{\frac{80\,{a}^{7}{b}^{3}}{3}{x}^{-{\frac{9}{2}}}}-9\,{\frac{{a}^{8}{b}^{2}}{{x}^{5}}}-{\frac{20\,{a}^{9}b}{11}{x}^{-{\frac{11}{2}}}}-{\frac{{a}^{10}}{6\,{x}^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^10/x^7,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43767, size = 151, normalized size = 3.28 \[ -\frac{66 \, b^{10} x^{5} + 440 \, a b^{9} x^{\frac{9}{2}} + 1485 \, a^{2} b^{8} x^{4} + 3168 \, a^{3} b^{7} x^{\frac{7}{2}} + 4620 \, a^{4} b^{6} x^{3} + 4752 \, a^{5} b^{5} x^{\frac{5}{2}} + 3465 \, a^{6} b^{4} x^{2} + 1760 \, a^{7} b^{3} x^{\frac{3}{2}} + 594 \, a^{8} b^{2} x + 120 \, a^{9} b \sqrt{x} + 11 \, a^{10}}{66 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^10/x^7,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.232941, size = 153, normalized size = 3.33 \[ -\frac{66 \, b^{10} x^{5} + 1485 \, a^{2} b^{8} x^{4} + 4620 \, a^{4} b^{6} x^{3} + 3465 \, a^{6} b^{4} x^{2} + 594 \, a^{8} b^{2} x + 11 \, a^{10} + 8 \,{\left (55 \, a b^{9} x^{4} + 396 \, a^{3} b^{7} x^{3} + 594 \, a^{5} b^{5} x^{2} + 220 \, a^{7} b^{3} x + 15 \, a^{9} b\right )} \sqrt{x}}{66 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^10/x^7,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 13.2353, size = 134, normalized size = 2.91 \[ - \frac{a^{10}}{6 x^{6}} - \frac{20 a^{9} b}{11 x^{\frac{11}{2}}} - \frac{9 a^{8} b^{2}}{x^{5}} - \frac{80 a^{7} b^{3}}{3 x^{\frac{9}{2}}} - \frac{105 a^{6} b^{4}}{2 x^{4}} - \frac{72 a^{5} b^{5}}{x^{\frac{7}{2}}} - \frac{70 a^{4} b^{6}}{x^{3}} - \frac{48 a^{3} b^{7}}{x^{\frac{5}{2}}} - \frac{45 a^{2} b^{8}}{2 x^{2}} - \frac{20 a b^{9}}{3 x^{\frac{3}{2}}} - \frac{b^{10}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**10/x**7,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21934, size = 151, normalized size = 3.28 \[ -\frac{66 \, b^{10} x^{5} + 440 \, a b^{9} x^{\frac{9}{2}} + 1485 \, a^{2} b^{8} x^{4} + 3168 \, a^{3} b^{7} x^{\frac{7}{2}} + 4620 \, a^{4} b^{6} x^{3} + 4752 \, a^{5} b^{5} x^{\frac{5}{2}} + 3465 \, a^{6} b^{4} x^{2} + 1760 \, a^{7} b^{3} x^{\frac{3}{2}} + 594 \, a^{8} b^{2} x + 120 \, a^{9} b \sqrt{x} + 11 \, a^{10}}{66 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^10/x^7,x, algorithm="giac")
[Out]