Optimal. Leaf size=17 \[ -\frac {a}{4 x^4}-\frac {b}{3 x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \[ -\frac {a}{4 x^4}-\frac {b}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^5} \, dx &=\int \left (\frac {a}{x^5}+\frac {b}{x^4}\right ) \, dx\\ &=-\frac {a}{4 x^4}-\frac {b}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ -\frac {a}{4 x^4}-\frac {b}{3 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 13, normalized size = 0.76 \[ -\frac {4 \, b x + 3 \, a}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.68, size = 13, normalized size = 0.76 \[ -\frac {4 \, b x + 3 \, a}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.82 \[ -\frac {b}{3 x^{3}}-\frac {a}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 13, normalized size = 0.76 \[ -\frac {4 \, b x + 3 \, a}{12 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.76 \[ -\frac {3\,a+4\,b\,x}{12\,x^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 14, normalized size = 0.82 \[ \frac {- 3 a - 4 b x}{12 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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