Optimal. Leaf size=17 \[ -\frac {a}{7 x^7}-\frac {b}{3 x^3} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {14}
\begin {gather*} -\frac {a}{7 x^7}-\frac {b}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^4}{x^8} \, dx &=\int \left (\frac {a}{x^8}+\frac {b}{x^4}\right ) \, dx\\ &=-\frac {a}{7 x^7}-\frac {b}{3 x^3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {a}{7 x^7}-\frac {b}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.82
method | result | size |
default | \(-\frac {a}{7 x^{7}}-\frac {b}{3 x^{3}}\) | \(14\) |
norman | \(\frac {-\frac {b \,x^{4}}{3}-\frac {a}{7}}{x^{7}}\) | \(15\) |
risch | \(\frac {-\frac {b \,x^{4}}{3}-\frac {a}{7}}{x^{7}}\) | \(15\) |
gosper | \(-\frac {7 b \,x^{4}+3 a}{21 x^{7}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 15, normalized size = 0.88 \begin {gather*} -\frac {7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 15, normalized size = 0.88 \begin {gather*} -\frac {7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} \frac {- 3 a - 7 b x^{4}}{21 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.85, size = 15, normalized size = 0.88 \begin {gather*} -\frac {7 \, b x^{4} + 3 \, a}{21 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 15, normalized size = 0.88 \begin {gather*} -\frac {7\,b\,x^4+3\,a}{21\,x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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