Optimal. Leaf size=17 \[ \frac {b x^3}{3}+\frac {a x^5}{5} \]
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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 x^5}{5}+\frac {b x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \left (a+\frac {b}{x^2}\right ) x^4 \, dx &=\int \left (b x^2+a x^4\right ) \, dx\\ &=\frac {b x^3}{3}+\frac {a x^5}{5}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {b x^3}{3}+\frac {a x^5}{5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 14, normalized size = 0.82
method | result | size |
default | \(\frac {1}{3} b \,x^{3}+\frac {1}{5} a \,x^{5}\) | \(14\) |
risch | \(\frac {1}{3} b \,x^{3}+\frac {1}{5} a \,x^{5}\) | \(14\) |
gosper | \(\frac {x^{3} \left (3 a \,x^{2}+5 b \right )}{15}\) | \(16\) |
norman | \(\frac {\frac {1}{3} b \,x^{4}+\frac {1}{5} x^{6} a}{x}\) | \(18\) |
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 {1}{5} \, a x^{5} + \frac {1}{3} \, b x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, a x^{5} + \frac {1}{3} \, b x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.71 \begin {gather*} \frac {a x^{5}}{5} + \frac {b x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.53, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{5} \, a x^{5} + \frac {1}{3} \, b x^{3} \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 = 0.76 \begin {gather*} \frac {a\,x^5}{5}+\frac {b\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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