Optimal. Leaf size=17 \[ -\frac {(a+b x)^3}{3 a x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, 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} \[ -\frac {(a+b x)^3}{3 a x^3} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^4} \, dx &=-\frac {(a+b x)^3}{3 a x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.53 \[ -\frac {a^2}{3 x^3}-\frac {a b}{x^2}-\frac {b^2}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 22, normalized size = 1.29 \[ -\frac {3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.48, size = 22, normalized size = 1.29 \[ -\frac {3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 1.47 \[ -\frac {b^{2}}{x}-\frac {a b}{x^{2}}-\frac {a^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 22, normalized size = 1.29 \[ -\frac {3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 22, normalized size = 1.29 \[ -\frac {\frac {a^2}{3}+a\,b\,x+b^2\,x^2}{x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 24, normalized size = 1.41 \[ \frac {- a^{2} - 3 a b x - 3 b^{2} x^{2}}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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