Optimal. Leaf size=17 \[ -\frac{(a+b x)^4}{4 a x^4} \]
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Rubi [A] time = 0.0016722, 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} \[ -\frac{(a+b x)^4}{4 a x^4} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{(a+b x)^3}{x^5} \, dx &=-\frac{(a+b x)^4}{4 a x^4}\\ \end{align*}
Mathematica [B] time = 0.0046872, size = 39, normalized size = 2.29 \[ -\frac{a^2 b}{x^3}-\frac{a^3}{4 x^4}-\frac{3 a b^2}{2 x^2}-\frac{b^3}{x} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 36, normalized size = 2.1 \begin{align*} -{\frac{{a}^{2}b}{{x}^{3}}}-{\frac{{a}^{3}}{4\,{x}^{4}}}-{\frac{3\,{b}^{2}a}{2\,{x}^{2}}}-{\frac{{b}^{3}}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.01065, size = 45, normalized size = 2.65 \begin{align*} -\frac{4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.61322, size = 73, normalized size = 4.29 \begin{align*} -\frac{4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.448039, size = 36, normalized size = 2.12 \begin{align*} - \frac{a^{3} + 4 a^{2} b x + 6 a b^{2} x^{2} + 4 b^{3} x^{3}}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.1902, size = 45, normalized size = 2.65 \begin{align*} -\frac{4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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