Optimal. Leaf size=17 \[ -\frac {(a+b x)^2}{2 a x^2} \]
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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 = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {37}
\begin {gather*} -\frac {(a+b x)^2}{2 a x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {a+b x}{x^3} \, dx &=-\frac {(a+b x)^2}{2 a x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.88 \begin {gather*} -\frac {a}{2 x^2}-\frac {b}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.82
method | result | size |
gosper | \(-\frac {2 b x +a}{2 x^{2}}\) | \(12\) |
norman | \(\frac {-b x -\frac {a}{2}}{x^{2}}\) | \(13\) |
risch | \(\frac {-b x -\frac {a}{2}}{x^{2}}\) | \(13\) |
default | \(-\frac {b}{x}-\frac {a}{2 x^{2}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2 \, b x + a}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.60, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2 \, b x + a}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} \frac {- a - 2 b x}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.64, size = 11, normalized size = 0.65 \begin {gather*} -\frac {2 \, b x + a}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 11, normalized size = 0.65 \begin {gather*} -\frac {a+2\,b\,x}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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