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 = 0.04, antiderivative size = 34, normalized size of antiderivative = 1.00, 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 14
Rule 1390
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*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.00 \[ \frac {1}{63} (3 x+2)^{21}+\frac {1}{42} (3 x+2)^{14}+\frac {1}{21} (3 x+2)^7 \]
Antiderivative was successfully verified.
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fricas [B] time = 0.75, size = 104, normalized size = 3.06 \[ \frac {1162261467}{7} x^{21} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac {15819767221203}{14} x^{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 28, normalized size = 0.82 \[ \frac {1}{63} \, {\left (3 \, x + 2\right )}^{21} + \frac {1}{42} \, {\left (3 \, x + 2\right )}^{14} + \frac {1}{21} \, {\left (3 \, x + 2\right )}^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 105, normalized size = 3.09 \[ \frac {1162261467}{7} x^{21}+2324522934 x^{20}+15496819560 x^{19}+65431015920 x^{18}+196293047760 x^{17}+444930908256 x^{16}+790988281344 x^{15}+\frac {15819767221203}{14} x^{14}+1318314865122 x^{13}+1269491970942 x^{12}+1015602174288 x^{11}+677082445416 x^{10}+376174427616 x^{9}+173635132896 x^{8}+66158154783 x^{7}+20588764518 x^{6}+5149786572 x^{5}+1010576952 x^{4}+149902032 x^{3}+15808800 x^{2}+1056832 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.54, size = 104, normalized size = 3.06 \[ \frac {1162261467}{7} \, x^{21} + 2324522934 \, x^{20} + 15496819560 \, x^{19} + 65431015920 \, x^{18} + 196293047760 \, x^{17} + 444930908256 \, x^{16} + 790988281344 \, x^{15} + \frac {15819767221203}{14} \, x^{14} + 1318314865122 \, x^{13} + 1269491970942 \, x^{12} + 1015602174288 \, x^{11} + 677082445416 \, x^{10} + 376174427616 \, x^{9} + 173635132896 \, x^{8} + 66158154783 \, x^{7} + 20588764518 \, x^{6} + 5149786572 \, x^{5} + 1010576952 \, x^{4} + 149902032 \, x^{3} + 15808800 \, x^{2} + 1056832 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.58, size = 29, normalized size = 0.85 \[ \frac {{\left (3\,x+2\right )}^7\,\left (3\,{\left (3\,x+2\right )}^7+2\,{\left (3\,x+2\right )}^{14}+6\right )}{126} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.10, size = 107, normalized size = 3.15 \[ \frac {1162261467 x^{21}}{7} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac {15819767221203 x^{14}}{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \]
Verification of antiderivative is not currently implemented for this CAS.
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