Optimal. Leaf size=17 \[ -\frac {b}{4 x^4}-\frac {c}{2 x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, 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*} -\frac {b}{4 x^4}-\frac {c}{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^7} \, dx &=\int \left (\frac {b}{x^5}+\frac {c}{x^3}\right ) \, dx\\ &=-\frac {b}{4 x^4}-\frac {c}{2 x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {b}{4 x^4}-\frac {c}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.82
method | result | size |
gosper | \(-\frac {2 c \,x^{2}+b}{4 x^{4}}\) | \(14\) |
default | \(-\frac {b}{4 x^{4}}-\frac {c}{2 x^{2}}\) | \(14\) |
risch | \(\frac {-\frac {c \,x^{2}}{2}-\frac {b}{4}}{x^{4}}\) | \(15\) |
norman | \(\frac {-\frac {1}{4} b \,x^{2}-\frac {1}{2} c \,x^{4}}{x^{6}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.76 \begin {gather*} -\frac {2 \, c x^{2} + b}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 13, normalized size = 0.76 \begin {gather*} -\frac {2 \, c x^{2} + b}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 14, normalized size = 0.82 \begin {gather*} \frac {- b - 2 c x^{2}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 6.04, size = 13, normalized size = 0.76 \begin {gather*} -\frac {2 \, c x^{2} + b}{4 \, x^{4}} \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 = 0.76 \begin {gather*} -\frac {2\,c\,x^2+b}{4\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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