Optimal. Leaf size=18 \[ -\frac {(1-2 x)^2}{22 (5 x+3)^2} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {37} \begin {gather*} -\frac {(1-2 x)^2}{22 (5 x+3)^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {1-2 x}{(3+5 x)^3} \, dx &=-\frac {(1-2 x)^2}{22 (3+5 x)^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.89 \begin {gather*} \frac {20 x+1}{50 (5 x+3)^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1-2 x}{(3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.64, size = 19, normalized size = 1.06 \begin {gather*} \frac {20 \, x + 1}{50 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 14, normalized size = 0.78 \begin {gather*} \frac {20 \, x + 1}{50 \, {\left (5 \, x + 3\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 20, normalized size = 1.11 \begin {gather*} -\frac {11}{50 \left (5 x +3\right )^{2}}+\frac {2}{25 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 19, normalized size = 1.06 \begin {gather*} \frac {20 \, x + 1}{50 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 14, normalized size = 0.78 \begin {gather*} \frac {20\,x+1}{50\,{\left (5\,x+3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.94 \begin {gather*} - \frac {- 20 x - 1}{1250 x^{2} + 1500 x + 450} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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