Optimal. Leaf size=86 \[ \frac{953535}{3 x+2}+\frac{617100}{5 x+3}+\frac{64317}{(3 x+2)^2}-\frac{33275}{2 (5 x+3)^2}+\frac{5236}{(3 x+2)^3}+\frac{1617}{4 (3 x+2)^4}+\frac{343}{15 (3 x+2)^5}-6618975 \log (3 x+2)+6618975 \log (5 x+3) \]
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Rubi [A] time = 0.0480218, antiderivative size = 86, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{953535}{3 x+2}+\frac{617100}{5 x+3}+\frac{64317}{(3 x+2)^2}-\frac{33275}{2 (5 x+3)^2}+\frac{5236}{(3 x+2)^3}+\frac{1617}{4 (3 x+2)^4}+\frac{343}{15 (3 x+2)^5}-6618975 \log (3 x+2)+6618975 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x)^6 (3+5 x)^3} \, dx &=\int \left (-\frac{343}{(2+3 x)^6}-\frac{4851}{(2+3 x)^5}-\frac{47124}{(2+3 x)^4}-\frac{385902}{(2+3 x)^3}-\frac{2860605}{(2+3 x)^2}-\frac{19856925}{2+3 x}+\frac{166375}{(3+5 x)^3}-\frac{3085500}{(3+5 x)^2}+\frac{33094875}{3+5 x}\right ) \, dx\\ &=\frac{343}{15 (2+3 x)^5}+\frac{1617}{4 (2+3 x)^4}+\frac{5236}{(2+3 x)^3}+\frac{64317}{(2+3 x)^2}+\frac{953535}{2+3 x}-\frac{33275}{2 (3+5 x)^2}+\frac{617100}{3+5 x}-6618975 \log (2+3 x)+6618975 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0648542, size = 88, normalized size = 1.02 \[ \frac{953535}{3 x+2}+\frac{617100}{5 x+3}+\frac{64317}{(3 x+2)^2}-\frac{33275}{2 (5 x+3)^2}+\frac{5236}{(3 x+2)^3}+\frac{1617}{4 (3 x+2)^4}+\frac{343}{15 (3 x+2)^5}-6618975 \log (5 (3 x+2))+6618975 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 81, normalized size = 0.9 \begin{align*}{\frac{343}{15\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{1617}{4\, \left ( 2+3\,x \right ) ^{4}}}+5236\, \left ( 2+3\,x \right ) ^{-3}+64317\, \left ( 2+3\,x \right ) ^{-2}+953535\, \left ( 2+3\,x \right ) ^{-1}-{\frac{33275}{2\, \left ( 3+5\,x \right ) ^{2}}}+617100\, \left ( 3+5\,x \right ) ^{-1}-6618975\,\ln \left ( 2+3\,x \right ) +6618975\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02518, size = 116, normalized size = 1.35 \begin{align*} \frac{160841092500 \, x^{6} + 627280260750 \, x^{5} + 1018898535600 \, x^{4} + 882286862985 \, x^{3} + 429553050280 \, x^{2} + 111486629505 \, x + 12050702538}{60 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} + 6618975 \, \log \left (5 \, x + 3\right ) - 6618975 \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.35695, size = 595, normalized size = 6.92 \begin{align*} \frac{160841092500 \, x^{6} + 627280260750 \, x^{5} + 1018898535600 \, x^{4} + 882286862985 \, x^{3} + 429553050280 \, x^{2} + 397138500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (5 \, x + 3\right ) - 397138500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (3 \, x + 2\right ) + 111486629505 \, x + 12050702538}{60 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.214785, size = 82, normalized size = 0.95 \begin{align*} \frac{160841092500 x^{6} + 627280260750 x^{5} + 1018898535600 x^{4} + 882286862985 x^{3} + 429553050280 x^{2} + 111486629505 x + 12050702538}{364500 x^{7} + 1652400 x^{6} + 3209220 x^{5} + 3461400 x^{4} + 2239200 x^{3} + 868800 x^{2} + 187200 x + 17280} + 6618975 \log{\left (x + \frac{3}{5} \right )} - 6618975 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.50877, size = 88, normalized size = 1.02 \begin{align*} \frac{160841092500 \, x^{6} + 627280260750 \, x^{5} + 1018898535600 \, x^{4} + 882286862985 \, x^{3} + 429553050280 \, x^{2} + 111486629505 \, x + 12050702538}{60 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{5}} + 6618975 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6618975 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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