Optimal. Leaf size=89 \[ -\frac{a^7}{7 x^7}-\frac{7 a^6 b}{6 x^6}-\frac{21 a^5 b^2}{5 x^5}-\frac{35 a^4 b^3}{4 x^4}-\frac{35 a^3 b^4}{3 x^3}-\frac{21 a^2 b^5}{2 x^2}-\frac{7 a b^6}{x}+b^7 \log (x) \]
[Out]
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Rubi [A] time = 0.0716816, antiderivative size = 89, 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 \[ -\frac{a^7}{7 x^7}-\frac{7 a^6 b}{6 x^6}-\frac{21 a^5 b^2}{5 x^5}-\frac{35 a^4 b^3}{4 x^4}-\frac{35 a^3 b^4}{3 x^3}-\frac{21 a^2 b^5}{2 x^2}-\frac{7 a b^6}{x}+b^7 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^7/x^8,x]
[Out]
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Rubi in Sympy [A] time = 14.7544, size = 88, normalized size = 0.99 \[ - \frac{a^{7}}{7 x^{7}} - \frac{7 a^{6} b}{6 x^{6}} - \frac{21 a^{5} b^{2}}{5 x^{5}} - \frac{35 a^{4} b^{3}}{4 x^{4}} - \frac{35 a^{3} b^{4}}{3 x^{3}} - \frac{21 a^{2} b^{5}}{2 x^{2}} - \frac{7 a b^{6}}{x} + b^{7} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**7/x**8,x)
[Out]
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Mathematica [A] time = 0.0059792, size = 89, normalized size = 1. \[ -\frac{a^7}{7 x^7}-\frac{7 a^6 b}{6 x^6}-\frac{21 a^5 b^2}{5 x^5}-\frac{35 a^4 b^3}{4 x^4}-\frac{35 a^3 b^4}{3 x^3}-\frac{21 a^2 b^5}{2 x^2}-\frac{7 a b^6}{x}+b^7 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^7/x^8,x]
[Out]
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Maple [A] time = 0.012, size = 78, normalized size = 0.9 \[ -{\frac{{a}^{7}}{7\,{x}^{7}}}-{\frac{7\,{a}^{6}b}{6\,{x}^{6}}}-{\frac{21\,{a}^{5}{b}^{2}}{5\,{x}^{5}}}-{\frac{35\,{a}^{4}{b}^{3}}{4\,{x}^{4}}}-{\frac{35\,{a}^{3}{b}^{4}}{3\,{x}^{3}}}-{\frac{21\,{a}^{2}{b}^{5}}{2\,{x}^{2}}}-7\,{\frac{a{b}^{6}}{x}}+{b}^{7}\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^7/x^8,x)
[Out]
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Maxima [A] time = 1.34241, size = 105, normalized size = 1.18 \[ b^{7} \log \left (x\right ) - \frac{2940 \, a b^{6} x^{6} + 4410 \, a^{2} b^{5} x^{5} + 4900 \, a^{3} b^{4} x^{4} + 3675 \, a^{4} b^{3} x^{3} + 1764 \, a^{5} b^{2} x^{2} + 490 \, a^{6} b x + 60 \, a^{7}}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.196088, size = 109, normalized size = 1.22 \[ \frac{420 \, b^{7} x^{7} \log \left (x\right ) - 2940 \, a b^{6} x^{6} - 4410 \, a^{2} b^{5} x^{5} - 4900 \, a^{3} b^{4} x^{4} - 3675 \, a^{4} b^{3} x^{3} - 1764 \, a^{5} b^{2} x^{2} - 490 \, a^{6} b x - 60 \, a^{7}}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.4695, size = 82, normalized size = 0.92 \[ b^{7} \log{\left (x \right )} - \frac{60 a^{7} + 490 a^{6} b x + 1764 a^{5} b^{2} x^{2} + 3675 a^{4} b^{3} x^{3} + 4900 a^{3} b^{4} x^{4} + 4410 a^{2} b^{5} x^{5} + 2940 a b^{6} x^{6}}{420 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**7/x**8,x)
[Out]
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GIAC/XCAS [A] time = 0.220656, size = 107, normalized size = 1.2 \[ b^{7}{\rm ln}\left ({\left | x \right |}\right ) - \frac{2940 \, a b^{6} x^{6} + 4410 \, a^{2} b^{5} x^{5} + 4900 \, a^{3} b^{4} x^{4} + 3675 \, a^{4} b^{3} x^{3} + 1764 \, a^{5} b^{2} x^{2} + 490 \, a^{6} b x + 60 \, a^{7}}{420 \, x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7/x^8,x, algorithm="giac")
[Out]