Optimal. Leaf size=17 \[ -\frac{(a+b x)^6}{6 a x^6} \]
[Out]
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Rubi [A] time = 0.0113885, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{(a+b x)^6}{6 a x^6} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^5/x^7,x]
[Out]
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Rubi in Sympy [A] time = 2.26342, size = 14, normalized size = 0.82 \[ - \frac{\left (a + b x\right )^{6}}{6 a x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**5/x**7,x)
[Out]
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Mathematica [B] time = 0.00548291, size = 65, normalized size = 3.82 \[ -\frac{a^5}{6 x^6}-\frac{a^4 b}{x^5}-\frac{5 a^3 b^2}{2 x^4}-\frac{10 a^2 b^3}{3 x^3}-\frac{5 a b^4}{2 x^2}-\frac{b^5}{x} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^5/x^7,x]
[Out]
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Maple [B] time = 0.009, size = 58, normalized size = 3.4 \[ -{\frac{5\,a{b}^{4}}{2\,{x}^{2}}}-{\frac{{b}^{5}}{x}}-{\frac{10\,{a}^{2}{b}^{3}}{3\,{x}^{3}}}-{\frac{{a}^{5}}{6\,{x}^{6}}}-{\frac{5\,{a}^{3}{b}^{2}}{2\,{x}^{4}}}-{\frac{{a}^{4}b}{{x}^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^5/x^7,x)
[Out]
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Maxima [A] time = 1.35964, size = 74, normalized size = 4.35 \[ -\frac{6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.191183, size = 74, normalized size = 4.35 \[ -\frac{6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.99232, size = 60, normalized size = 3.53 \[ - \frac{a^{5} + 6 a^{4} b x + 15 a^{3} b^{2} x^{2} + 20 a^{2} b^{3} x^{3} + 15 a b^{4} x^{4} + 6 b^{5} x^{5}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**5/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.207411, size = 74, normalized size = 4.35 \[ -\frac{6 \, b^{5} x^{5} + 15 \, a b^{4} x^{4} + 20 \, a^{2} b^{3} x^{3} + 15 \, a^{3} b^{2} x^{2} + 6 \, a^{4} b x + a^{5}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^5/x^7,x, algorithm="giac")
[Out]