Optimal. Leaf size=13 \[ -\frac {b}{2 x^2}+c \log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14}
\begin {gather*} c \log (x)-\frac {b}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x^5} \, dx &=\int \left (\frac {b}{x^3}+\frac {c}{x}\right ) \, dx\\ &=-\frac {b}{2 x^2}+c \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} -\frac {b}{2 x^2}+c \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 0.92
method | result | size |
default | \(-\frac {b}{2 x^{2}}+c \ln \left (x \right )\) | \(12\) |
norman | \(-\frac {b}{2 x^{2}}+c \ln \left (x \right )\) | \(12\) |
risch | \(-\frac {b}{2 x^{2}}+c \ln \left (x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 14, normalized size = 1.08 \begin {gather*} \frac {1}{2} \, c \log \left (x^{2}\right ) - \frac {b}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 17, normalized size = 1.31 \begin {gather*} \frac {2 \, c x^{2} \log \left (x\right ) - b}{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 = 10, normalized size = 0.77 \begin {gather*} - \frac {b}{2 x^{2}} + c \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.84, size = 20, normalized size = 1.54 \begin {gather*} \frac {1}{2} \, c \log \left (x^{2}\right ) - \frac {c x^{2} + b}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 11, normalized size = 0.85 \begin {gather*} c\,\ln \left (x\right )-\frac {b}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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