Optimal. Leaf size=32 \[ a c x+\frac {1}{2} a d x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4 \]
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Rubi [A] time = 0.03, antiderivative size = 32, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 54, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {1586} \[ a c x+\frac {1}{2} a d x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4 \]
Antiderivative was successfully verified.
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Rule 1586
Rubi steps
\begin {align*} \int \frac {a^2 c+a^2 d x+2 a b c x^2+2 a b d x^3+b^2 c x^4+b^2 d x^5}{a+b x^2} \, dx &=\int \left (a c+a d x+b c x^2+b d x^3\right ) \, dx\\ &=a c x+\frac {1}{2} a d x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.00 \[ a c x+\frac {1}{2} a d x^2+\frac {1}{3} b c x^3+\frac {1}{4} b d x^4 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 26, normalized size = 0.81 \[ \frac {1}{4} \, b d x^{4} + \frac {1}{3} \, b c x^{3} + \frac {1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 26, normalized size = 0.81 \[ \frac {1}{4} \, b d x^{4} + \frac {1}{3} \, b c x^{3} + \frac {1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 27, normalized size = 0.84 \[ \frac {1}{4} b d \,x^{4}+\frac {1}{3} b c \,x^{3}+\frac {1}{2} a d \,x^{2}+a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.78, size = 26, normalized size = 0.81 \[ \frac {1}{4} \, b d x^{4} + \frac {1}{3} \, b c x^{3} + \frac {1}{2} \, a d x^{2} + a c x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 26, normalized size = 0.81 \[ \frac {b\,d\,x^4}{4}+\frac {b\,c\,x^3}{3}+\frac {a\,d\,x^2}{2}+a\,c\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 29, normalized size = 0.91 \[ a c x + \frac {a d x^{2}}{2} + \frac {b c x^{3}}{3} + \frac {b d x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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