Optimal. Leaf size=17 \[ -\frac{(a+b x)^6}{6 a x^6} \]
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Rubi [A] time = 0.0016275, 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, Rules used = {37} \[ -\frac{(a+b x)^6}{6 a x^6} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^5}{x^7} \, dx &=-\frac{(a+b x)^6}{6 a x^6}\\ \end{align*}
Mathematica [B] time = 0.0087569, size = 65, normalized size = 3.82 \[ -\frac{5 a^3 b^2}{2 x^4}-\frac{10 a^2 b^3}{3 x^3}-\frac{a^4 b}{x^5}-\frac{a^5}{6 x^6}-\frac{5 a b^4}{2 x^2}-\frac{b^5}{x} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.006, size = 58, normalized size = 3.4 \begin{align*} -{\frac{10\,{a}^{2}{b}^{3}}{3\,{x}^{3}}}-{\frac{{a}^{4}b}{{x}^{5}}}-{\frac{5\,{a}^{3}{b}^{2}}{2\,{x}^{4}}}-{\frac{{a}^{5}}{6\,{x}^{6}}}-{\frac{5\,a{b}^{4}}{2\,{x}^{2}}}-{\frac{{b}^{5}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.05717, size = 74, normalized size = 4.35 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.51836, size = 120, normalized size = 7.06 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.613611, size = 60, normalized size = 3.53 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.20617, size = 74, normalized size = 4.35 \begin{align*} -\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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