Optimal. Leaf size=34 \[ \frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]
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Rubi [A] time = 0.0356623, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {1390, 14} \[ \frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 1390
Rule 14
Rubi steps
\begin{align*} \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x^6 \left (1+x^7+x^{14}\right ) \, dx,x,2+3 x\right )\\ &=\frac{1}{3} \operatorname{Subst}\left (\int \left (x^6+x^{13}+x^{20}\right ) \, dx,x,2+3 x\right )\\ &=\frac{1}{21} (2+3 x)^7+\frac{1}{42} (2+3 x)^{14}+\frac{1}{63} (2+3 x)^{21}\\ \end{align*}
Mathematica [A] time = 0.0132572, size = 34, normalized size = 1. \[ \frac{1}{63} (3 x+2)^{21}+\frac{1}{42} (3 x+2)^{14}+\frac{1}{21} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 105, normalized size = 3.1 \begin{align*}{\frac{1162261467\,{x}^{21}}{7}}+2324522934\,{x}^{20}+15496819560\,{x}^{19}+65431015920\,{x}^{18}+196293047760\,{x}^{17}+444930908256\,{x}^{16}+790988281344\,{x}^{15}+{\frac{15819767221203\,{x}^{14}}{14}}+1318314865122\,{x}^{13}+1269491970942\,{x}^{12}+1015602174288\,{x}^{11}+677082445416\,{x}^{10}+376174427616\,{x}^{9}+173635132896\,{x}^{8}+66158154783\,{x}^{7}+20588764518\,{x}^{6}+5149786572\,{x}^{5}+1010576952\,{x}^{4}+149902032\,{x}^{3}+15808800\,{x}^{2}+1056832\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.969965, size = 140, normalized size = 4.12 \begin{align*} \frac{1162261467}{7} \, x^{21} + 2324522934 \, x^{20} + 15496819560 \, x^{19} + 65431015920 \, x^{18} + 196293047760 \, x^{17} + 444930908256 \, x^{16} + 790988281344 \, x^{15} + \frac{15819767221203}{14} \, x^{14} + 1318314865122 \, x^{13} + 1269491970942 \, x^{12} + 1015602174288 \, x^{11} + 677082445416 \, x^{10} + 376174427616 \, x^{9} + 173635132896 \, x^{8} + 66158154783 \, x^{7} + 20588764518 \, x^{6} + 5149786572 \, x^{5} + 1010576952 \, x^{4} + 149902032 \, x^{3} + 15808800 \, x^{2} + 1056832 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.07722, size = 532, normalized size = 15.65 \begin{align*} \frac{1162261467}{7} x^{21} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac{15819767221203}{14} x^{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.092468, size = 107, normalized size = 3.15 \begin{align*} \frac{1162261467 x^{21}}{7} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac{15819767221203 x^{14}}{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08124, size = 38, normalized size = 1.12 \begin{align*} \frac{1}{63} \,{\left (3 \, x + 2\right )}^{21} + \frac{1}{42} \,{\left (3 \, x + 2\right )}^{14} + \frac{1}{21} \,{\left (3 \, x + 2\right )}^{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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