Optimal. Leaf size=44 \[ \frac {50 x^7}{7}+\frac {35 x^6}{6}+\frac {103 x^5}{5}+\frac {85 x^4}{4}+\frac {83 x^3}{3}+16 x^2+12 x \]
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Rubi [A] time = 0.03, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1657} \[ \frac {50 x^7}{7}+\frac {35 x^6}{6}+\frac {103 x^5}{5}+\frac {85 x^4}{4}+\frac {83 x^3}{3}+16 x^2+12 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right )^2 \, dx &=\int \left (12+32 x+83 x^2+85 x^3+103 x^4+35 x^5+50 x^6\right ) \, dx\\ &=12 x+16 x^2+\frac {83 x^3}{3}+\frac {85 x^4}{4}+\frac {103 x^5}{5}+\frac {35 x^6}{6}+\frac {50 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 44, normalized size = 1.00 \[ \frac {50 x^7}{7}+\frac {35 x^6}{6}+\frac {103 x^5}{5}+\frac {85 x^4}{4}+\frac {83 x^3}{3}+16 x^2+12 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 34, normalized size = 0.77 \[ \frac {50}{7} x^{7} + \frac {35}{6} x^{6} + \frac {103}{5} x^{5} + \frac {85}{4} x^{4} + \frac {83}{3} x^{3} + 16 x^{2} + 12 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 34, normalized size = 0.77 \[ \frac {50}{7} \, x^{7} + \frac {35}{6} \, x^{6} + \frac {103}{5} \, x^{5} + \frac {85}{4} \, x^{4} + \frac {83}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.80 \[ \frac {50}{7} x^{7}+\frac {35}{6} x^{6}+\frac {103}{5} x^{5}+\frac {85}{4} x^{4}+\frac {83}{3} x^{3}+16 x^{2}+12 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 34, normalized size = 0.77 \[ \frac {50}{7} \, x^{7} + \frac {35}{6} \, x^{6} + \frac {103}{5} \, x^{5} + \frac {85}{4} \, x^{4} + \frac {83}{3} \, x^{3} + 16 \, x^{2} + 12 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.77 \[ \frac {50\,x^7}{7}+\frac {35\,x^6}{6}+\frac {103\,x^5}{5}+\frac {85\,x^4}{4}+\frac {83\,x^3}{3}+16\,x^2+12\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 41, normalized size = 0.93 \[ \frac {50 x^{7}}{7} + \frac {35 x^{6}}{6} + \frac {103 x^{5}}{5} + \frac {85 x^{4}}{4} + \frac {83 x^{3}}{3} + 16 x^{2} + 12 x \]
Verification of antiderivative is not currently implemented for this CAS.
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