Optimal. Leaf size=15 \[ -\frac {a}{4 x^4}-\frac {b}{x} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} -\frac {a}{4 x^4}-\frac {b}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^3}{x^5} \, dx &=\int \left (\frac {a}{x^5}+\frac {b}{x^2}\right ) \, dx\\ &=-\frac {a}{4 x^4}-\frac {b}{x}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} -\frac {a}{4 x^4}-\frac {b}{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 | \(-\frac {4 b \,x^{3}+a}{4 x^{4}}\) | \(14\) |
default | \(-\frac {a}{4 x^{4}}-\frac {b}{x}\) | \(14\) |
norman | \(\frac {-b \,x^{3}-\frac {a}{4}}{x^{4}}\) | \(15\) |
risch | \(\frac {-b \,x^{3}-\frac {a}{4}}{x^{4}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.87 \begin {gather*} -\frac {4 \, b x^{3} + a}{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 = 0.87 \begin {gather*} -\frac {4 \, b x^{3} + a}{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 = 0.93 \begin {gather*} \frac {- a - 4 b x^{3}}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.18, size = 13, normalized size = 0.87 \begin {gather*} -\frac {4 \, b x^{3} + a}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 13, normalized size = 0.87 \begin {gather*} -\frac {4\,b\,x^3+a}{4\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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