Optimal. Leaf size=18 \[ -\frac {a}{x}+b x+\frac {c x^3}{3} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \begin {gather*} -\frac {a}{x}+b x+\frac {c x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a x+b x^3+c x^5}{x^3} \, dx &=\int \left (b+\frac {a}{x^2}+c x^2\right ) \, dx\\ &=-\frac {a}{x}+b x+\frac {c x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \begin {gather*} -\frac {a}{x}+b x+\frac {c x^3}{3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a x+b x^3+c x^5}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.02, size = 20, normalized size = 1.11 \begin {gather*} \frac {c x^{4} + 3 \, b x^{2} - 3 \, a}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.59, size = 16, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, c x^{3} + b x - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.94 \begin {gather*} \frac {c \,x^{3}}{3}+b x -\frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 16, normalized size = 0.89 \begin {gather*} \frac {1}{3} \, c x^{3} + b x - \frac {a}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 16, normalized size = 0.89 \begin {gather*} b\,x-\frac {a}{x}+\frac {c\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.67 \begin {gather*} - \frac {a}{x} + b x + \frac {c x^{3}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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