Optimal. Leaf size=37 \[ \frac {7}{5 x+3}-\frac {11}{10 (5 x+3)^2}-21 \log (3 x+2)+21 \log (5 x+3) \]
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Rubi [A] time = 0.02, 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 = {77} \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 77
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 = 0.02, size = 48, normalized size = 1.30 \begin {gather*} \frac {350 x-210 (5 x+3)^2 \log (5 (3 x+2))+210 (5 x+3)^2 \log (5 x+3)+199}{10 (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}{(2+3 x) (3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.80, 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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giac [A] time = 1.23, 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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maple [A] time = 0.01, size = 36, normalized size = 0.97 \begin {gather*} -21 \ln \left (3 x +2\right )+21 \ln \left (5 x +3\right )-\frac {11}{10 \left (5 x +3\right )^{2}}+\frac {7}{5 x +3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, 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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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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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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