Optimal. Leaf size=15 \[ -\frac {a}{3 x^3}-\frac {b}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, 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}{3 x^3}-\frac {b}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^2}{x^4} \, dx &=\int \left (\frac {a}{x^4}+\frac {b}{x^2}\right ) \, dx\\ &=-\frac {a}{3 x^3}-\frac {b}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {a}{3 x^3}-\frac {b}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.93
method | result | size |
gosper | \(-\frac {3 b \,x^{2}+a}{3 x^{3}}\) | \(14\) |
default | \(-\frac {a}{3 x^{3}}-\frac {b}{x}\) | \(14\) |
norman | \(\frac {-b \,x^{2}-\frac {a}{3}}{x^{3}}\) | \(15\) |
risch | \(\frac {-b \,x^{2}-\frac {a}{3}}{x^{3}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3 \, b x^{2} + a}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.95, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3 \, b x^{2} + a}{3 \, 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 = 0.93 \begin {gather*} \frac {- a - 3 b x^{2}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.58, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3 \, b x^{2} + a}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3\,b\,x^2+a}{3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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