Optimal. Leaf size=61 \[ -\frac{a^5}{5 x^5}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{3 x^3}-\frac{5 a^2 b^3}{x^2}-\frac{5 a b^4}{x}+b^5 \log (x) \]
[Out]
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Rubi [A] time = 0.0508431, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a^5}{5 x^5}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{3 x^3}-\frac{5 a^2 b^3}{x^2}-\frac{5 a b^4}{x}+b^5 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/x^6,x]
[Out]
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Rubi in Sympy [A] time = 10.121, size = 60, normalized size = 0.98 \[ - \frac{a^{5}}{5 x^{5}} - \frac{5 a^{4} b}{4 x^{4}} - \frac{10 a^{3} b^{2}}{3 x^{3}} - \frac{5 a^{2} b^{3}}{x^{2}} - \frac{5 a b^{4}}{x} + b^{5} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/x**6,x)
[Out]
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Mathematica [A] time = 0.00579649, size = 61, normalized size = 1. \[ -\frac{a^5}{5 x^5}-\frac{5 a^4 b}{4 x^4}-\frac{10 a^3 b^2}{3 x^3}-\frac{5 a^2 b^3}{x^2}-\frac{5 a b^4}{x}+b^5 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/x^6,x]
[Out]
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Maple [A] time = 0.01, size = 56, normalized size = 0.9 \[ -{\frac{{a}^{5}}{5\,{x}^{5}}}-{\frac{5\,{a}^{4}b}{4\,{x}^{4}}}-{\frac{10\,{a}^{3}{b}^{2}}{3\,{x}^{3}}}-5\,{\frac{{a}^{2}{b}^{3}}{{x}^{2}}}-5\,{\frac{a{b}^{4}}{x}}+{b}^{5}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/x^6,x)
[Out]
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Maxima [A] time = 1.3342, size = 76, normalized size = 1.25 \[ b^{5} \log \left (x\right ) - \frac{300 \, a b^{4} x^{4} + 300 \, a^{2} b^{3} x^{3} + 200 \, a^{3} b^{2} x^{2} + 75 \, a^{4} b x + 12 \, a^{5}}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201568, size = 80, normalized size = 1.31 \[ \frac{60 \, b^{5} x^{5} \log \left (x\right ) - 300 \, a b^{4} x^{4} - 300 \, a^{2} b^{3} x^{3} - 200 \, a^{3} b^{2} x^{2} - 75 \, a^{4} b x - 12 \, a^{5}}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.86133, size = 58, normalized size = 0.95 \[ b^{5} \log{\left (x \right )} - \frac{12 a^{5} + 75 a^{4} b x + 200 a^{3} b^{2} x^{2} + 300 a^{2} b^{3} x^{3} + 300 a b^{4} x^{4}}{60 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.207086, size = 77, normalized size = 1.26 \[ b^{5}{\rm ln}\left ({\left | x \right |}\right ) - \frac{300 \, a b^{4} x^{4} + 300 \, a^{2} b^{3} x^{3} + 200 \, a^{3} b^{2} x^{2} + 75 \, a^{4} b x + 12 \, a^{5}}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^6,x, algorithm="giac")
[Out]