Optimal. Leaf size=15 \[ -\frac {d}{a+b x+c x^2} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {629} \[ -\frac {d}{a+b x+c x^2} \]
Antiderivative was successfully verified.
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Rule 629
Rubi steps
\begin {align*} \int \frac {b d+2 c d x}{\left (a+b x+c x^2\right )^2} \, dx &=-\frac {d}{a+b x+c x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.93 \[ -\frac {d}{a+x (b+c x)} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.08, size = 15, normalized size = 1.00 \[ -\frac {d}{c x^{2} + b x + a} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 22, normalized size = 1.47 \[ -\frac {d}{a + \frac {c d x^{2} + b d x}{d}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 1.07 \[ -\frac {d}{c \,x^{2}+b x +a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 15, normalized size = 1.00 \[ -\frac {d}{c x^{2} + b x + a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.42, size = 15, normalized size = 1.00 \[ -\frac {d}{c\,x^2+b\,x+a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 12, normalized size = 0.80 \[ - \frac {d}{a + b x + c x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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