Optimal. Leaf size=37 \[ -\frac {11}{10 (3+5 x)^2}+\frac {7}{3+5 x}-21 \log (2+3 x)+21 \log (3+5 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {7}{5 x+3}-\frac {11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac {63}{2+3 x}+\frac {11}{(3+5 x)^3}-\frac {35}{(3+5 x)^2}+\frac {105}{3+5 x}\right ) \, dx\\ &=-\frac {11}{10 (3+5 x)^2}+\frac {7}{3+5 x}-21 \log (2+3 x)+21 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 48, normalized size = 1.30 \begin {gather*} \frac {199+350 x-210 (3+5 x)^2 \log (5 (2+3 x))+210 (3+5 x)^2 \log (3+5 x)}{10 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 36, normalized size = 0.97
method | result | size |
risch | \(\frac {35 x +\frac {199}{10}}{\left (3+5 x \right )^{2}}-21 \ln \left (2+3 x \right )+21 \ln \left (3+5 x \right )\) | \(32\) |
norman | \(\frac {-\frac {94}{3} x -\frac {995}{18} x^{2}}{\left (3+5 x \right )^{2}}-21 \ln \left (2+3 x \right )+21 \ln \left (3+5 x \right )\) | \(35\) |
default | \(-\frac {11}{10 \left (3+5 x \right )^{2}}+\frac {7}{3+5 x}-21 \ln \left (2+3 x \right )+21 \ln \left (3+5 x \right )\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 36, normalized size = 0.97 \begin {gather*} \frac {350 \, x + 199}{10 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + 21 \, \log \left (5 \, x + 3\right ) - 21 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.65, size = 55, normalized size = 1.49 \begin {gather*} \frac {210 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 210 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 350 \, x + 199}{10 \, {\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 = 0.14, size = 32, normalized size = 0.86 \begin {gather*} - \frac {- 350 x - 199}{250 x^{2} + 300 x + 90} + 21 \log {\left (x + \frac {3}{5} \right )} - 21 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.54, size = 33, normalized size = 0.89 \begin {gather*} \frac {350 \, x + 199}{10 \, {\left (5 \, x + 3\right )}^{2}} + 21 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 21 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 25, normalized size = 0.68 \begin {gather*} \frac {\frac {7\,x}{5}+\frac {199}{250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-42\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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