Optimal. Leaf size=37 \[ \frac {3 (5 x+3)^3}{4 (3 x+2)^3}+\frac {7 (5 x+3)^3}{12 (3 x+2)^4} \]
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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 = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {78, 37} \begin {gather*} \frac {3 (5 x+3)^3}{4 (3 x+2)^3}+\frac {7 (5 x+3)^3}{12 (3 x+2)^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^5} \, dx &=\frac {7 (3+5 x)^3}{12 (2+3 x)^4}+\frac {9}{4} \int \frac {(3+5 x)^2}{(2+3 x)^4} \, dx\\ &=\frac {7 (3+5 x)^3}{12 (2+3 x)^4}+\frac {3 (3+5 x)^3}{4 (2+3 x)^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 0.70 \begin {gather*} \frac {600 x^3+810 x^2+312 x+25}{36 (3 x+2)^4} \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) (3+5 x)^2}{(2+3 x)^5} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.80, size = 39, normalized size = 1.05 \begin {gather*} \frac {600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 37, normalized size = 1.00 \begin {gather*} \frac {50}{81 \, {\left (3 \, x + 2\right )}} - \frac {65}{54 \, {\left (3 \, x + 2\right )}^{2}} + \frac {8}{27 \, {\left (3 \, x + 2\right )}^{3}} - \frac {7}{324 \, {\left (3 \, x + 2\right )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 38, normalized size = 1.03 \begin {gather*} \frac {8}{27 \left (3 x +2\right )^{3}}-\frac {7}{324 \left (3 x +2\right )^{4}}-\frac {65}{54 \left (3 x +2\right )^{2}}+\frac {50}{81 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 39, normalized size = 1.05 \begin {gather*} \frac {600 \, x^{3} + 810 \, x^{2} + 312 \, x + 25}{36 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 37, normalized size = 1.00 \begin {gather*} \frac {50}{81\,\left (3\,x+2\right )}-\frac {65}{54\,{\left (3\,x+2\right )}^2}+\frac {8}{27\,{\left (3\,x+2\right )}^3}-\frac {7}{324\,{\left (3\,x+2\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 37, normalized size = 1.00 \begin {gather*} - \frac {- 600 x^{3} - 810 x^{2} - 312 x - 25}{2916 x^{4} + 7776 x^{3} + 7776 x^{2} + 3456 x + 576} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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