Optimal. Leaf size=15 \[ -\frac {b}{3 x^3}-\frac {c}{x} \]
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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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14}
\begin {gather*} -\frac {b}{3 x^3}-\frac {c}{x} \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^6} \, dx &=\int \left (\frac {b}{x^4}+\frac {c}{x^2}\right ) \, dx\\ &=-\frac {b}{3 x^3}-\frac {c}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {b}{3 x^3}-\frac {c}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.93
method | result | size |
gosper | \(-\frac {3 c \,x^{2}+b}{3 x^{3}}\) | \(14\) |
default | \(-\frac {b}{3 x^{3}}-\frac {c}{x}\) | \(14\) |
risch | \(\frac {-c \,x^{2}-\frac {b}{3}}{x^{3}}\) | \(15\) |
norman | \(\frac {-\frac {1}{3} b \,x^{2}-c \,x^{4}}{x^{5}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3 \, c x^{2} + b}{3 \, x^{3}} \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 = 0.87 \begin {gather*} -\frac {3 \, c x^{2} + b}{3 \, x^{3}} \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 = 0.93 \begin {gather*} \frac {- b - 3 c x^{2}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 6.83, size = 13, normalized size = 0.87 \begin {gather*} -\frac {3 \, c x^{2} + b}{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\,c\,x^2+b}{3\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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