Optimal. Leaf size=46 \[ a c \log (x)+a d x+\frac {1}{2} a e x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4+\frac {1}{5} b e x^5 \]
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Rubi [A] time = 0.02, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1628} \[ a c \log (x)+a d x+\frac {1}{2} a e x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4+\frac {1}{5} b e x^5 \]
Antiderivative was successfully verified.
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Rule 1628
Rubi steps
\begin {align*} \int \frac {\left (c+d x+e x^2\right ) \left (a+b x^3\right )}{x} \, dx &=\int \left (a d+\frac {a c}{x}+a e x+b c x^2+b d x^3+b e x^4\right ) \, dx\\ &=a d x+\frac {1}{2} a e x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4+\frac {1}{5} b e x^5+a c \log (x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 46, normalized size = 1.00 \[ a c \log (x)+a d x+\frac {1}{2} a e x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4+\frac {1}{5} b e x^5 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 38, normalized size = 0.83 \[ \frac {1}{5} \, b e x^{5} + \frac {1}{4} \, b d x^{4} + \frac {1}{3} \, b c x^{3} + \frac {1}{2} \, a e x^{2} + a d x + a c \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 41, normalized size = 0.89 \[ \frac {1}{5} \, b x^{5} e + \frac {1}{4} \, b d x^{4} + \frac {1}{3} \, b c x^{3} + \frac {1}{2} \, a x^{2} e + a d x + a c \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 39, normalized size = 0.85 \[ \frac {b e \,x^{5}}{5}+\frac {b d \,x^{4}}{4}+\frac {b c \,x^{3}}{3}+\frac {a e \,x^{2}}{2}+a c \ln \relax (x )+a d x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 38, normalized size = 0.83 \[ \frac {1}{5} \, b e x^{5} + \frac {1}{4} \, b d x^{4} + \frac {1}{3} \, b c x^{3} + \frac {1}{2} \, a e x^{2} + a d x + a c \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 38, normalized size = 0.83 \[ a\,c\,\ln \relax (x)+a\,d\,x+\frac {b\,c\,x^3}{3}+\frac {a\,e\,x^2}{2}+\frac {b\,d\,x^4}{4}+\frac {b\,e\,x^5}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 44, normalized size = 0.96 \[ a c \log {\relax (x )} + a d x + \frac {a e x^{2}}{2} + \frac {b c x^{3}}{3} + \frac {b d x^{4}}{4} + \frac {b e x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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