Optimal. Leaf size=15 \[ -\frac{d}{a+b x+c x^2} \]
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Rubi [A] time = 0.0051263, antiderivative size = 15, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0039089, size = 14, normalized size = 0.93 \[ -\frac{d}{a+x (b+c x)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.037, size = 16, normalized size = 1.1 \begin{align*} -{\frac{d}{c{x}^{2}+bx+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05552, size = 20, normalized size = 1.33 \begin{align*} -\frac{d}{c x^{2} + b x + a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.93995, size = 30, normalized size = 2. \begin{align*} -\frac{d}{c x^{2} + b x + a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.594069, size = 12, normalized size = 0.8 \begin{align*} - \frac{d}{a + b x + c x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18969, size = 20, normalized size = 1.33 \begin{align*} -\frac{d}{c x^{2} + b x + a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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