Optimal. Leaf size=57 \[ -\frac{a^5}{4 x^4}-\frac{5 a^4 b}{3 x^3}-\frac{5 a^3 b^2}{x^2}-\frac{10 a^2 b^3}{x}+5 a b^4 \log (x)+b^5 x \]
[Out]
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Rubi [A] time = 0.0507979, antiderivative size = 57, 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 \[ -\frac{a^5}{4 x^4}-\frac{5 a^4 b}{3 x^3}-\frac{5 a^3 b^2}{x^2}-\frac{10 a^2 b^3}{x}+5 a b^4 \log (x)+b^5 x \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/x^5,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{5}}{4 x^{4}} - \frac{5 a^{4} b}{3 x^{3}} - \frac{5 a^{3} b^{2}}{x^{2}} - \frac{10 a^{2} b^{3}}{x} + 5 a b^{4} \log{\left (x \right )} + \int b^{5}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/x**5,x)
[Out]
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Mathematica [A] time = 0.00828468, size = 57, normalized size = 1. \[ -\frac{a^5}{4 x^4}-\frac{5 a^4 b}{3 x^3}-\frac{5 a^3 b^2}{x^2}-\frac{10 a^2 b^3}{x}+5 a b^4 \log (x)+b^5 x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/x^5,x]
[Out]
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Maple [A] time = 0.01, size = 54, normalized size = 1. \[ -{\frac{{a}^{5}}{4\,{x}^{4}}}-{\frac{5\,{a}^{4}b}{3\,{x}^{3}}}-5\,{\frac{{a}^{3}{b}^{2}}{{x}^{2}}}-10\,{\frac{{a}^{2}{b}^{3}}{x}}+{b}^{5}x+5\,a{b}^{4}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/x^5,x)
[Out]
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Maxima [A] time = 1.34581, size = 73, normalized size = 1.28 \[ b^{5} x + 5 \, a b^{4} \log \left (x\right ) - \frac{120 \, a^{2} b^{3} x^{3} + 60 \, a^{3} b^{2} x^{2} + 20 \, a^{4} b x + 3 \, a^{5}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201102, size = 80, normalized size = 1.4 \[ \frac{12 \, b^{5} x^{5} + 60 \, a b^{4} x^{4} \log \left (x\right ) - 120 \, a^{2} b^{3} x^{3} - 60 \, a^{3} b^{2} x^{2} - 20 \, a^{4} b x - 3 \, a^{5}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.83429, size = 56, normalized size = 0.98 \[ 5 a b^{4} \log{\left (x \right )} + b^{5} x - \frac{3 a^{5} + 20 a^{4} b x + 60 a^{3} b^{2} x^{2} + 120 a^{2} b^{3} x^{3}}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.212931, size = 74, normalized size = 1.3 \[ b^{5} x + 5 \, a b^{4}{\rm ln}\left ({\left | x \right |}\right ) - \frac{120 \, a^{2} b^{3} x^{3} + 60 \, a^{3} b^{2} x^{2} + 20 \, a^{4} b x + 3 \, a^{5}}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^5,x, algorithm="giac")
[Out]