Optimal. Leaf size=96 \[ \frac{b^3 \left (a+b \sqrt{x}\right )^{11}}{2002 a^4 x^{11/2}}-\frac{b^2 \left (a+b \sqrt{x}\right )^{11}}{182 a^3 x^6}+\frac{3 b \left (a+b \sqrt{x}\right )^{11}}{91 a^2 x^{13/2}}-\frac{\left (a+b \sqrt{x}\right )^{11}}{7 a x^7} \]
[Out]
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Rubi [A] time = 0.106826, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{b^3 \left (a+b \sqrt{x}\right )^{11}}{2002 a^4 x^{11/2}}-\frac{b^2 \left (a+b \sqrt{x}\right )^{11}}{182 a^3 x^6}+\frac{3 b \left (a+b \sqrt{x}\right )^{11}}{91 a^2 x^{13/2}}-\frac{\left (a+b \sqrt{x}\right )^{11}}{7 a x^7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*Sqrt[x])^10/x^8,x]
[Out]
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Rubi in Sympy [A] time = 12.058, size = 85, normalized size = 0.89 \[ - \frac{\left (a + b \sqrt{x}\right )^{11}}{7 a x^{7}} + \frac{3 b \left (a + b \sqrt{x}\right )^{11}}{91 a^{2} x^{\frac{13}{2}}} - \frac{b^{2} \left (a + b \sqrt{x}\right )^{11}}{182 a^{3} x^{6}} + \frac{b^{3} \left (a + b \sqrt{x}\right )^{11}}{2002 a^{4} x^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b*x**(1/2))**10/x**8,x)
[Out]
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Mathematica [A] time = 0.0444066, size = 124, normalized size = 1.29 \[ -\frac{286 a^{10}+3080 a^9 b \sqrt{x}+15015 a^8 b^2 x+43680 a^7 b^3 x^{3/2}+84084 a^6 b^4 x^2+112112 a^5 b^5 x^{5/2}+105105 a^4 b^6 x^3+68640 a^3 b^7 x^{7/2}+30030 a^2 b^8 x^4+8008 a b^9 x^{9/2}+1001 b^{10} x^5}{2002 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*Sqrt[x])^10/x^8,x]
[Out]
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Maple [A] time = 0.004, size = 113, normalized size = 1.2 \[ -{\frac{{b}^{10}}{2\,{x}^{2}}}-4\,{\frac{a{b}^{9}}{{x}^{5/2}}}-15\,{\frac{{a}^{2}{b}^{8}}{{x}^{3}}}-{\frac{240\,{a}^{3}{b}^{7}}{7}{x}^{-{\frac{7}{2}}}}-{\frac{105\,{a}^{4}{b}^{6}}{2\,{x}^{4}}}-56\,{\frac{{a}^{5}{b}^{5}}{{x}^{9/2}}}-42\,{\frac{{a}^{6}{b}^{4}}{{x}^{5}}}-{\frac{240\,{a}^{7}{b}^{3}}{11}{x}^{-{\frac{11}{2}}}}-{\frac{15\,{a}^{8}{b}^{2}}{2\,{x}^{6}}}-{\frac{20\,{a}^{9}b}{13}{x}^{-{\frac{13}{2}}}}-{\frac{{a}^{10}}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b*x^(1/2))^10/x^8,x)
[Out]
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Maxima [A] time = 1.44842, size = 151, normalized size = 1.57 \[ -\frac{1001 \, b^{10} x^{5} + 8008 \, a b^{9} x^{\frac{9}{2}} + 30030 \, a^{2} b^{8} x^{4} + 68640 \, a^{3} b^{7} x^{\frac{7}{2}} + 105105 \, a^{4} b^{6} x^{3} + 112112 \, a^{5} b^{5} x^{\frac{5}{2}} + 84084 \, a^{6} b^{4} x^{2} + 43680 \, a^{7} b^{3} x^{\frac{3}{2}} + 15015 \, a^{8} b^{2} x + 3080 \, a^{9} b \sqrt{x} + 286 \, a^{10}}{2002 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^10/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234056, size = 153, normalized size = 1.59 \[ -\frac{1001 \, b^{10} x^{5} + 30030 \, a^{2} b^{8} x^{4} + 105105 \, a^{4} b^{6} x^{3} + 84084 \, a^{6} b^{4} x^{2} + 15015 \, a^{8} b^{2} x + 286 \, a^{10} + 8 \,{\left (1001 \, a b^{9} x^{4} + 8580 \, a^{3} b^{7} x^{3} + 14014 \, a^{5} b^{5} x^{2} + 5460 \, a^{7} b^{3} x + 385 \, a^{9} b\right )} \sqrt{x}}{2002 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^10/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.4966, size = 138, normalized size = 1.44 \[ - \frac{a^{10}}{7 x^{7}} - \frac{20 a^{9} b}{13 x^{\frac{13}{2}}} - \frac{15 a^{8} b^{2}}{2 x^{6}} - \frac{240 a^{7} b^{3}}{11 x^{\frac{11}{2}}} - \frac{42 a^{6} b^{4}}{x^{5}} - \frac{56 a^{5} b^{5}}{x^{\frac{9}{2}}} - \frac{105 a^{4} b^{6}}{2 x^{4}} - \frac{240 a^{3} b^{7}}{7 x^{\frac{7}{2}}} - \frac{15 a^{2} b^{8}}{x^{3}} - \frac{4 a b^{9}}{x^{\frac{5}{2}}} - \frac{b^{10}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b*x**(1/2))**10/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.216388, size = 151, normalized size = 1.57 \[ -\frac{1001 \, b^{10} x^{5} + 8008 \, a b^{9} x^{\frac{9}{2}} + 30030 \, a^{2} b^{8} x^{4} + 68640 \, a^{3} b^{7} x^{\frac{7}{2}} + 105105 \, a^{4} b^{6} x^{3} + 112112 \, a^{5} b^{5} x^{\frac{5}{2}} + 84084 \, a^{6} b^{4} x^{2} + 43680 \, a^{7} b^{3} x^{\frac{3}{2}} + 15015 \, a^{8} b^{2} x + 3080 \, a^{9} b \sqrt{x} + 286 \, a^{10}}{2002 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*sqrt(x) + a)^10/x^8,x, algorithm="giac")
[Out]