Optimal. Leaf size=56 \[ 24 x+50 x^2+\frac {322 x^3}{3}+\frac {579 x^4}{4}+\frac {876 x^5}{5}+134 x^6+\frac {720 x^7}{7}+\frac {325 x^8}{8}+\frac {250 x^9}{9} \]
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Rubi [A]
time = 0.03, antiderivative size = 56, 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 = {1671}
\begin {gather*} \frac {250 x^9}{9}+\frac {325 x^8}{8}+\frac {720 x^7}{7}+134 x^6+\frac {876 x^5}{5}+\frac {579 x^4}{4}+\frac {322 x^3}{3}+50 x^2+24 x \end {gather*}
Antiderivative was successfully verified.
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Rule 1671
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right )^3 \, dx &=\int \left (24+100 x+322 x^2+579 x^3+876 x^4+804 x^5+720 x^6+325 x^7+250 x^8\right ) \, dx\\ &=24 x+50 x^2+\frac {322 x^3}{3}+\frac {579 x^4}{4}+\frac {876 x^5}{5}+134 x^6+\frac {720 x^7}{7}+\frac {325 x^8}{8}+\frac {250 x^9}{9}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 56, normalized size = 1.00 \begin {gather*} 24 x+50 x^2+\frac {322 x^3}{3}+\frac {579 x^4}{4}+\frac {876 x^5}{5}+134 x^6+\frac {720 x^7}{7}+\frac {325 x^8}{8}+\frac {250 x^9}{9} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 45, normalized size = 0.80
method | result | size |
gosper | \(24 x +50 x^{2}+\frac {322}{3} x^{3}+\frac {579}{4} x^{4}+\frac {876}{5} x^{5}+134 x^{6}+\frac {720}{7} x^{7}+\frac {325}{8} x^{8}+\frac {250}{9} x^{9}\) | \(45\) |
default | \(24 x +50 x^{2}+\frac {322}{3} x^{3}+\frac {579}{4} x^{4}+\frac {876}{5} x^{5}+134 x^{6}+\frac {720}{7} x^{7}+\frac {325}{8} x^{8}+\frac {250}{9} x^{9}\) | \(45\) |
norman | \(24 x +50 x^{2}+\frac {322}{3} x^{3}+\frac {579}{4} x^{4}+\frac {876}{5} x^{5}+134 x^{6}+\frac {720}{7} x^{7}+\frac {325}{8} x^{8}+\frac {250}{9} x^{9}\) | \(45\) |
risch | \(24 x +50 x^{2}+\frac {322}{3} x^{3}+\frac {579}{4} x^{4}+\frac {876}{5} x^{5}+134 x^{6}+\frac {720}{7} x^{7}+\frac {325}{8} x^{8}+\frac {250}{9} x^{9}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 44, normalized size = 0.79 \begin {gather*} \frac {250}{9} \, x^{9} + \frac {325}{8} \, x^{8} + \frac {720}{7} \, x^{7} + 134 \, x^{6} + \frac {876}{5} \, x^{5} + \frac {579}{4} \, x^{4} + \frac {322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 4.22, size = 44, normalized size = 0.79 \begin {gather*} \frac {250}{9} \, x^{9} + \frac {325}{8} \, x^{8} + \frac {720}{7} \, x^{7} + 134 \, x^{6} + \frac {876}{5} \, x^{5} + \frac {579}{4} \, x^{4} + \frac {322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 53, normalized size = 0.95 \begin {gather*} \frac {250 x^{9}}{9} + \frac {325 x^{8}}{8} + \frac {720 x^{7}}{7} + 134 x^{6} + \frac {876 x^{5}}{5} + \frac {579 x^{4}}{4} + \frac {322 x^{3}}{3} + 50 x^{2} + 24 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.94, size = 44, normalized size = 0.79 \begin {gather*} \frac {250}{9} \, x^{9} + \frac {325}{8} \, x^{8} + \frac {720}{7} \, x^{7} + 134 \, x^{6} + \frac {876}{5} \, x^{5} + \frac {579}{4} \, x^{4} + \frac {322}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 44, normalized size = 0.79 \begin {gather*} \frac {250\,x^9}{9}+\frac {325\,x^8}{8}+\frac {720\,x^7}{7}+134\,x^6+\frac {876\,x^5}{5}+\frac {579\,x^4}{4}+\frac {322\,x^3}{3}+50\,x^2+24\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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