Optimal. Leaf size=43 \[ -\frac {4 x^4}{3}+\frac {32 x^3}{27}+\frac {1156 x^2}{27}+\frac {11576 x}{81}-6 \log (x+1)+\frac {10625}{243} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {800, 632, 31} \begin {gather*} -\frac {4 x^4}{3}+\frac {32 x^3}{27}+\frac {1156 x^2}{27}+\frac {11576 x}{81}-6 \log (x+1)+\frac {10625}{243} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 632
Rule 800
Rubi steps
\begin {align*} \int \frac {(5-x) (3+2 x)^4}{2+5 x+3 x^2} \, dx &=\int \left (\frac {11576}{81}+\frac {2312 x}{27}+\frac {32 x^2}{9}-\frac {16 x^3}{3}+\frac {9653+9167 x}{81 \left (2+5 x+3 x^2\right )}\right ) \, dx\\ &=\frac {11576 x}{81}+\frac {1156 x^2}{27}+\frac {32 x^3}{27}-\frac {4 x^4}{3}+\frac {1}{81} \int \frac {9653+9167 x}{2+5 x+3 x^2} \, dx\\ &=\frac {11576 x}{81}+\frac {1156 x^2}{27}+\frac {32 x^3}{27}-\frac {4 x^4}{3}-18 \int \frac {1}{3+3 x} \, dx+\frac {10625}{81} \int \frac {1}{2+3 x} \, dx\\ &=\frac {11576 x}{81}+\frac {1156 x^2}{27}+\frac {32 x^3}{27}-\frac {4 x^4}{3}-6 \log (1+x)+\frac {10625}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 1.00 \begin {gather*} \frac {1}{972} \left (42500 \log (-6 x-4)-3 \left (432 x^4-384 x^3-13872 x^2-46304 x+1944 \log (-2 (x+1))-41727\right )\right ) \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 {(5-x) (3+2 x)^4}{2+5 x+3 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.60, size = 33, normalized size = 0.77 \begin {gather*} -\frac {4}{3} \, x^{4} + \frac {32}{27} \, x^{3} + \frac {1156}{27} \, x^{2} + \frac {11576}{81} \, x + \frac {10625}{243} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 35, normalized size = 0.81 \begin {gather*} -\frac {4}{3} \, x^{4} + \frac {32}{27} \, x^{3} + \frac {1156}{27} \, x^{2} + \frac {11576}{81} \, x + \frac {10625}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - 6 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 34, normalized size = 0.79 \begin {gather*} -\frac {4 x^{4}}{3}+\frac {32 x^{3}}{27}+\frac {1156 x^{2}}{27}+\frac {11576 x}{81}+\frac {10625 \ln \left (3 x +2\right )}{243}-6 \ln \left (x +1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 33, normalized size = 0.77 \begin {gather*} -\frac {4}{3} \, x^{4} + \frac {32}{27} \, x^{3} + \frac {1156}{27} \, x^{2} + \frac {11576}{81} \, x + \frac {10625}{243} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 31, normalized size = 0.72 \begin {gather*} \frac {11576\,x}{81}-6\,\ln \left (x+1\right )+\frac {10625\,\ln \left (x+\frac {2}{3}\right )}{243}+\frac {1156\,x^2}{27}+\frac {32\,x^3}{27}-\frac {4\,x^4}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 41, normalized size = 0.95 \begin {gather*} - \frac {4 x^{4}}{3} + \frac {32 x^{3}}{27} + \frac {1156 x^{2}}{27} + \frac {11576 x}{81} + \frac {10625 \log {\left (x + \frac {2}{3} \right )}}{243} - 6 \log {\left (x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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