Optimal. Leaf size=21 \[ -\frac {3 x+2}{2 \left (2 x^2+7 x+4\right )} \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {1660, 8} \[ -\frac {3 x+2}{2 \left (2 x^2+7 x+4\right )} \]
Antiderivative was successfully verified.
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Rule 8
Rule 1660
Rubi steps
\begin {align*} \int \frac {1+4 x+3 x^2}{\left (4+7 x+2 x^2\right )^2} \, dx &=-\frac {2+3 x}{2 \left (4+7 x+2 x^2\right )}-\frac {\int 0 \, dx}{17}\\ &=-\frac {2+3 x}{2 \left (4+7 x+2 x^2\right )}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \frac {-3 x-2}{2 \left (2 x^2+7 x+4\right )} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 19, normalized size = 0.90 \[ -\frac {3 \, x + 2}{2 \, {\left (2 \, x^{2} + 7 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 19, normalized size = 0.90 \[ -\frac {3 \, x + 2}{2 \, {\left (2 \, x^{2} + 7 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.81 \[ \frac {-\frac {3 x}{4}-\frac {1}{2}}{x^{2}+\frac {7}{2} x +2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 19, normalized size = 0.90 \[ -\frac {3 \, x + 2}{2 \, {\left (2 \, x^{2} + 7 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.84, size = 17, normalized size = 0.81 \[ -\frac {\frac {3\,x}{4}+\frac {1}{2}}{x^2+\frac {7\,x}{2}+2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 15, normalized size = 0.71 \[ \frac {- 3 x - 2}{4 x^{2} + 14 x + 8} \]
Verification of antiderivative is not currently implemented for this CAS.
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