Optimal. Leaf size=4 \[ c \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 4, 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, 29}
\begin {gather*} c \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 29
Rubi steps
\begin {align*} \int \frac {a c+b c x^2}{x \left (a+b x^2\right )} \, dx &=c \int \frac {1}{x} \, dx\\ &=c \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 4, normalized size = 1.00 \begin {gather*} c \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 5, normalized size = 1.25
method | result | size |
default | \(c \ln \left (x \right )\) | \(5\) |
norman | \(c \ln \left (x \right )\) | \(5\) |
risch | \(c \ln \left (x \right )\) | \(5\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 7, normalized size = 1.75 \begin {gather*} \frac {1}{2} \, c \log \left (x^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.08, size = 4, normalized size = 1.00 \begin {gather*} c \log \left (x\right ) \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 = 0.75 \begin {gather*} c \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.49, size = 5, normalized size = 1.25 \begin {gather*} c \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 4, normalized size = 1.00 \begin {gather*} c\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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