Optimal. Leaf size=54 \[ \frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3) \]
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Rubi [A] time = 0.0257839, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {44} \[ \frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{(2+x)^3 (3+x)^4} \, dx &=\int \left (\frac{1}{(2+x)^3}-\frac{4}{(2+x)^2}+\frac{10}{2+x}-\frac{1}{(3+x)^4}-\frac{3}{(3+x)^3}-\frac{6}{(3+x)^2}-\frac{10}{3+x}\right ) \, dx\\ &=-\frac{1}{2 (2+x)^2}+\frac{4}{2+x}+\frac{1}{3 (3+x)^3}+\frac{3}{2 (3+x)^2}+\frac{6}{3+x}+10 \log (2+x)-10 \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0145087, size = 54, normalized size = 1. \[ \frac{4}{x+2}+\frac{6}{x+3}-\frac{1}{2 (x+2)^2}+\frac{3}{2 (x+3)^2}+\frac{1}{3 (x+3)^3}+10 \log (x+2)-10 \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 49, normalized size = 0.9 \begin{align*} -{\frac{1}{2\, \left ( 2+x \right ) ^{2}}}+4\, \left ( 2+x \right ) ^{-1}+{\frac{1}{3\, \left ( 3+x \right ) ^{3}}}+{\frac{3}{2\, \left ( 3+x \right ) ^{2}}}+6\, \left ( 3+x \right ) ^{-1}+10\,\ln \left ( 2+x \right ) -10\,\ln \left ( 3+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.928574, size = 81, normalized size = 1.5 \begin{align*} \frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} + 4175 \, x + 2627}{6 \,{\left (x^{5} + 13 \, x^{4} + 67 \, x^{3} + 171 \, x^{2} + 216 \, x + 108\right )}} - 10 \, \log \left (x + 3\right ) + 10 \, \log \left (x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.26756, size = 306, normalized size = 5.67 \begin{align*} \frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} - 60 \,{\left (x^{5} + 13 \, x^{4} + 67 \, x^{3} + 171 \, x^{2} + 216 \, x + 108\right )} \log \left (x + 3\right ) + 60 \,{\left (x^{5} + 13 \, x^{4} + 67 \, x^{3} + 171 \, x^{2} + 216 \, x + 108\right )} \log \left (x + 2\right ) + 4175 \, x + 2627}{6 \,{\left (x^{5} + 13 \, x^{4} + 67 \, x^{3} + 171 \, x^{2} + 216 \, x + 108\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.159292, size = 58, normalized size = 1.07 \begin{align*} \frac{60 x^{4} + 630 x^{3} + 2450 x^{2} + 4175 x + 2627}{6 x^{5} + 78 x^{4} + 402 x^{3} + 1026 x^{2} + 1296 x + 648} + 10 \log{\left (x + 2 \right )} - 10 \log{\left (x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05268, size = 63, normalized size = 1.17 \begin{align*} \frac{60 \, x^{4} + 630 \, x^{3} + 2450 \, x^{2} + 4175 \, x + 2627}{6 \,{\left (x + 3\right )}^{3}{\left (x + 2\right )}^{2}} - 10 \, \log \left ({\left | x + 3 \right |}\right ) + 10 \, \log \left ({\left | x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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