Optimal. Leaf size=18 \[ -\frac {(1-2 x)^2}{22 (3+5 x)^2} \]
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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 {1+20 x}{50 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 20, normalized size = 1.11
method | result | size |
gosper | \(\frac {1+20 x}{50 \left (3+5 x \right )^{2}}\) | \(15\) |
risch | \(\frac {\frac {2 x}{5}+\frac {1}{50}}{\left (3+5 x \right )^{2}}\) | \(15\) |
norman | \(\frac {\frac {1}{3} x -\frac {1}{18} x^{2}}{\left (3+5 x \right )^{2}}\) | \(18\) |
default | \(\frac {2}{25 \left (3+5 x \right )}-\frac {11}{50 \left (3+5 x \right )^{2}}\) | \(20\) |
meijerg | \(\frac {x \left (\frac {5 x}{3}+2\right )}{54 \left (1+\frac {5 x}{3}\right )^{2}}-\frac {x^{2}}{27 \left (1+\frac {5 x}{3}\right )^{2}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, 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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Fricas [A]
time = 0.95, 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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Sympy [A]
time = 0.07, 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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Giac [A]
time = 0.57, 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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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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