Optimal. Leaf size=21 \[ -\frac {2 (35 x+29)}{\sqrt {3 x^2+5 x+2}} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {636} \begin {gather*} -\frac {2 (35 x+29)}{\sqrt {3 x^2+5 x+2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 636
Rubi steps
\begin {align*} \int \frac {5-x}{\left (2+5 x+3 x^2\right )^{3/2}} \, dx &=-\frac {2 (29+35 x)}{\sqrt {2+5 x+3 x^2}}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 21, normalized size = 1.00 \begin {gather*} -\frac {2 (35 x+29)}{\sqrt {3 x^2+5 x+2}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.30, size = 33, normalized size = 1.57 \begin {gather*} -\frac {2 (35 x+29) \sqrt {3 x^2+5 x+2}}{(x+1) (3 x+2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 19, normalized size = 0.90 \begin {gather*} -\frac {2 \, {\left (35 \, x + 29\right )}}{\sqrt {3 \, x^{2} + 5 \, x + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 19, normalized size = 0.90 \begin {gather*} -\frac {2 \, {\left (35 \, x + 29\right )}}{\sqrt {3 \, x^{2} + 5 \, x + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 1.33 \begin {gather*} -\frac {2 \left (35 x +29\right ) \left (x +1\right ) \left (3 x +2\right )}{\left (3 x^{2}+5 x +2\right )^{\frac {3}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 30, normalized size = 1.43 \begin {gather*} -\frac {70 \, x}{\sqrt {3 \, x^{2} + 5 \, x + 2}} - \frac {58}{\sqrt {3 \, x^{2} + 5 \, x + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 19, normalized size = 0.90 \begin {gather*} -\frac {2\,\left (35\,x+29\right )}{\sqrt {3\,x^2+5\,x+2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - \int \frac {x}{3 x^{2} \sqrt {3 x^{2} + 5 x + 2} + 5 x \sqrt {3 x^{2} + 5 x + 2} + 2 \sqrt {3 x^{2} + 5 x + 2}}\, dx - \int \left (- \frac {5}{3 x^{2} \sqrt {3 x^{2} + 5 x + 2} + 5 x \sqrt {3 x^{2} + 5 x + 2} + 2 \sqrt {3 x^{2} + 5 x + 2}}\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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