Optimal. Leaf size=6 \[ -\frac {c}{x} \]
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Rubi [A]
time = 0.00, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {21, 30}
\begin {gather*} -\frac {c}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 30
Rubi steps
\begin {align*} \int \frac {a c+b c x^2}{x^2 \left (a+b x^2\right )} \, dx &=c \int \frac {1}{x^2} \, dx\\ &=-\frac {c}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 6, normalized size = 1.00 \begin {gather*} -\frac {c}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 7, normalized size = 1.17
method | result | size |
gosper | \(-\frac {c}{x}\) | \(7\) |
default | \(-\frac {c}{x}\) | \(7\) |
norman | \(-\frac {c}{x}\) | \(7\) |
risch | \(-\frac {c}{x}\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 6, normalized size = 1.00 \begin {gather*} -\frac {c}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.06, size = 6, normalized size = 1.00 \begin {gather*} -\frac {c}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 3, normalized size = 0.50 \begin {gather*} - \frac {c}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.25, size = 6, normalized size = 1.00 \begin {gather*} -\frac {c}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 6, normalized size = 1.00 \begin {gather*} -\frac {c}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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