Optimal. Leaf size=17 \[ -\frac {b}{3 x^3}-\frac {a}{2 x^2} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} -\frac {a}{2 x^2}-\frac {b}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+\frac {b}{x}}{x^3} \, dx &=\int \left (\frac {b}{x^4}+\frac {a}{x^3}\right ) \, dx\\ &=-\frac {b}{3 x^3}-\frac {a}{2 x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {b}{3 x^3}-\frac {a}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.82
method | result | size |
norman | \(\frac {-\frac {a x}{2}-\frac {b}{3}}{x^{3}}\) | \(13\) |
risch | \(\frac {-\frac {a x}{2}-\frac {b}{3}}{x^{3}}\) | \(13\) |
gosper | \(-\frac {3 a x +2 b}{6 x^{3}}\) | \(14\) |
default | \(-\frac {b}{3 x^{3}}-\frac {a}{2 x^{2}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3 \, a x + 2 \, b}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3 \, a x + 2 \, b}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 14, normalized size = 0.82 \begin {gather*} \frac {- 3 a x - 2 b}{6 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.59, size = 13, normalized size = 0.76 \begin {gather*} -\frac {3 \, a x + 2 \, b}{6 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 13, normalized size = 0.76 \begin {gather*} -\frac {2\,b+3\,a\,x}{6\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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