Optimal. Leaf size=94 \[ a^8 x+8 a^7 b \log (x)-\frac{28 a^6 b^2}{x}-\frac{28 a^5 b^3}{x^2}-\frac{70 a^4 b^4}{3 x^3}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{5 x^5}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7} \]
[Out]
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Rubi [A] time = 0.105179, antiderivative size = 94, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ a^8 x+8 a^7 b \log (x)-\frac{28 a^6 b^2}{x}-\frac{28 a^5 b^3}{x^2}-\frac{70 a^4 b^4}{3 x^3}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{5 x^5}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x)^8,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 8 a^{7} b \log{\left (x \right )} - \frac{28 a^{6} b^{2}}{x} - \frac{28 a^{5} b^{3}}{x^{2}} - \frac{70 a^{4} b^{4}}{3 x^{3}} - \frac{14 a^{3} b^{5}}{x^{4}} - \frac{28 a^{2} b^{6}}{5 x^{5}} - \frac{4 a b^{7}}{3 x^{6}} - \frac{b^{8}}{7 x^{7}} + \int a^{8}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x)**8,x)
[Out]
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Mathematica [A] time = 0.00891505, size = 94, normalized size = 1. \[ a^8 x+8 a^7 b \log (x)-\frac{28 a^6 b^2}{x}-\frac{28 a^5 b^3}{x^2}-\frac{70 a^4 b^4}{3 x^3}-\frac{14 a^3 b^5}{x^4}-\frac{28 a^2 b^6}{5 x^5}-\frac{4 a b^7}{3 x^6}-\frac{b^8}{7 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x)^8,x]
[Out]
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Maple [A] time = 0.011, size = 87, normalized size = 0.9 \[ -{\frac{{b}^{8}}{7\,{x}^{7}}}-{\frac{4\,a{b}^{7}}{3\,{x}^{6}}}-{\frac{28\,{a}^{2}{b}^{6}}{5\,{x}^{5}}}-14\,{\frac{{a}^{3}{b}^{5}}{{x}^{4}}}-{\frac{70\,{a}^{4}{b}^{4}}{3\,{x}^{3}}}-28\,{\frac{{a}^{5}{b}^{3}}{{x}^{2}}}-28\,{\frac{{a}^{6}{b}^{2}}{x}}+{a}^{8}x+8\,{a}^{7}b\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x)^8,x)
[Out]
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Maxima [A] time = 1.44189, size = 117, normalized size = 1.24 \[ a^{8} x + 8 \, a^{7} b \log \left (x\right ) - \frac{2940 \, a^{6} b^{2} x^{6} + 2940 \, a^{5} b^{3} x^{5} + 2450 \, a^{4} b^{4} x^{4} + 1470 \, a^{3} b^{5} x^{3} + 588 \, a^{2} b^{6} x^{2} + 140 \, a b^{7} x + 15 \, b^{8}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218617, size = 124, normalized size = 1.32 \[ \frac{105 \, a^{8} x^{8} + 840 \, a^{7} b x^{7} \log \left (x\right ) - 2940 \, a^{6} b^{2} x^{6} - 2940 \, a^{5} b^{3} x^{5} - 2450 \, a^{4} b^{4} x^{4} - 1470 \, a^{3} b^{5} x^{3} - 588 \, a^{2} b^{6} x^{2} - 140 \, a b^{7} x - 15 \, b^{8}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.62155, size = 92, normalized size = 0.98 \[ a^{8} x + 8 a^{7} b \log{\left (x \right )} - \frac{2940 a^{6} b^{2} x^{6} + 2940 a^{5} b^{3} x^{5} + 2450 a^{4} b^{4} x^{4} + 1470 a^{3} b^{5} x^{3} + 588 a^{2} b^{6} x^{2} + 140 a b^{7} x + 15 b^{8}}{105 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.222334, size = 119, normalized size = 1.27 \[ a^{8} x + 8 \, a^{7} b{\rm ln}\left ({\left | x \right |}\right ) - \frac{2940 \, a^{6} b^{2} x^{6} + 2940 \, a^{5} b^{3} x^{5} + 2450 \, a^{4} b^{4} x^{4} + 1470 \, a^{3} b^{5} x^{3} + 588 \, a^{2} b^{6} x^{2} + 140 \, a b^{7} x + 15 \, b^{8}}{105 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x)^8,x, algorithm="giac")
[Out]