Optimal. Leaf size=17 \[ -\frac {(a+b x)^4}{4 a x^4} \]
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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} \begin {gather*} -\frac {(a+b x)^4}{4 a x^4} \end {gather*}
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*}
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Mathematica [B] time = 0.00, size = 39, normalized size = 2.29 \begin {gather*} -\frac {a^3}{4 x^4}-\frac {a^2 b}{x^3}-\frac {3 a b^2}{2 x^2}-\frac {b^3}{x} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b x)^3}{x^5} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [B] time = 1.30, size = 33, normalized size = 1.94 \begin {gather*} -\frac {4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.29, size = 33, normalized size = 1.94 \begin {gather*} -\frac {4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.01, size = 36, normalized size = 2.12 \begin {gather*} -\frac {b^{3}}{x}-\frac {3 a \,b^{2}}{2 x^{2}}-\frac {a^{2} b}{x^{3}}-\frac {a^{3}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.33, size = 33, normalized size = 1.94 \begin {gather*} -\frac {4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 33, normalized size = 1.94 \begin {gather*} -\frac {\frac {a^3}{4}+a^2\,b\,x+\frac {3\,a\,b^2\,x^2}{2}+b^3\,x^3}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.26, size = 36, normalized size = 2.12 \begin {gather*} \frac {- a^{3} - 4 a^{2} b x - 6 a b^{2} x^{2} - 4 b^{3} x^{3}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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