Optimal. Leaf size=56 \[ \frac {100 (3 x+2)^9}{2187}-\frac {185}{486} (3 x+2)^8+\frac {503}{567} (3 x+2)^7-\frac {259}{729} (3 x+2)^6+\frac {49 (3 x+2)^5}{1215} \]
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Rubi [A] time = 0.02, antiderivative size = 56, normalized size of antiderivative = 1.00, 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} \[ \frac {100 (3 x+2)^9}{2187}-\frac {185}{486} (3 x+2)^8+\frac {503}{567} (3 x+2)^7-\frac {259}{729} (3 x+2)^6+\frac {49 (3 x+2)^5}{1215} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {49}{81} (2+3 x)^4-\frac {518}{81} (2+3 x)^5+\frac {503}{27} (2+3 x)^6-\frac {740}{81} (2+3 x)^7+\frac {100}{81} (2+3 x)^8\right ) \, dx\\ &=\frac {49 (2+3 x)^5}{1215}-\frac {259}{729} (2+3 x)^6+\frac {503}{567} (2+3 x)^7-\frac {185}{486} (2+3 x)^8+\frac {100 (2+3 x)^9}{2187}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 52, normalized size = 0.93 \[ 900 x^9+\frac {5805 x^8}{2}+\frac {21141 x^7}{7}+115 x^6-\frac {9791 x^5}{5}-1174 x^4+\frac {424 x^3}{3}+384 x^2+144 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 44, normalized size = 0.79 \[ 900 x^{9} + \frac {5805}{2} x^{8} + \frac {21141}{7} x^{7} + 115 x^{6} - \frac {9791}{5} x^{5} - 1174 x^{4} + \frac {424}{3} x^{3} + 384 x^{2} + 144 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 44, normalized size = 0.79 \[ 900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 45, normalized size = 0.80 \[ 900 x^{9}+\frac {5805}{2} x^{8}+\frac {21141}{7} x^{7}+115 x^{6}-\frac {9791}{5} x^{5}-1174 x^{4}+\frac {424}{3} x^{3}+384 x^{2}+144 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 44, normalized size = 0.79 \[ 900 \, x^{9} + \frac {5805}{2} \, x^{8} + \frac {21141}{7} \, x^{7} + 115 \, x^{6} - \frac {9791}{5} \, x^{5} - 1174 \, x^{4} + \frac {424}{3} \, x^{3} + 384 \, x^{2} + 144 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 44, normalized size = 0.79 \[ 900\,x^9+\frac {5805\,x^8}{2}+\frac {21141\,x^7}{7}+115\,x^6-\frac {9791\,x^5}{5}-1174\,x^4+\frac {424\,x^3}{3}+384\,x^2+144\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 49, normalized size = 0.88 \[ 900 x^{9} + \frac {5805 x^{8}}{2} + \frac {21141 x^{7}}{7} + 115 x^{6} - \frac {9791 x^{5}}{5} - 1174 x^{4} + \frac {424 x^{3}}{3} + 384 x^{2} + 144 x \]
Verification of antiderivative is not currently implemented for this CAS.
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