Integrand size = 24, antiderivative size = 34 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1}{21} (2+3 x)^7+\frac {1}{42} (2+3 x)^{14}+\frac {1}{63} (2+3 x)^{21} \]
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Time = 0.02 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {1404, 14} \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1}{63} (3 x+2)^{21}+\frac {1}{42} (3 x+2)^{14}+\frac {1}{21} (3 x+2)^7 \]
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Rule 14
Rule 1404
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \text {Subst}\left (\int x^6 \left (1+x^7+x^{14}\right ) \, dx,x,2+3 x\right ) \\ & = \frac {1}{3} \text {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*}
Time = 0.02 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1}{21} (2+3 x)^7+\frac {1}{42} (2+3 x)^{14}+\frac {1}{63} (2+3 x)^{21} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(103\) vs. \(2(28)=56\).
Time = 0.56 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.06
method | result | size |
gosper | \(\frac {x \left (2324522934 x^{20}+32543321076 x^{19}+216955473840 x^{18}+916034222880 x^{17}+2748102668640 x^{16}+6229032715584 x^{15}+11073835938816 x^{14}+15819767221203 x^{13}+18456408111708 x^{12}+17772887593188 x^{11}+14218430440032 x^{10}+9479154235824 x^{9}+5266441986624 x^{8}+2430891860544 x^{7}+926214166962 x^{6}+288242703252 x^{5}+72097012008 x^{4}+14148077328 x^{3}+2098628448 x^{2}+221323200 x +14795648\right )}{14}\) | \(104\) |
default | \(1056832 x +15808800 x^{2}+149902032 x^{3}+1010576952 x^{4}+5149786572 x^{5}+20588764518 x^{6}+66158154783 x^{7}+173635132896 x^{8}+376174427616 x^{9}+677082445416 x^{10}+1015602174288 x^{11}+1269491970942 x^{12}+1318314865122 x^{13}+\frac {15819767221203}{14} x^{14}+790988281344 x^{15}+444930908256 x^{16}+196293047760 x^{17}+65431015920 x^{18}+15496819560 x^{19}+2324522934 x^{20}+\frac {1162261467}{7} x^{21}\) | \(105\) |
norman | \(1056832 x +15808800 x^{2}+149902032 x^{3}+1010576952 x^{4}+5149786572 x^{5}+20588764518 x^{6}+66158154783 x^{7}+173635132896 x^{8}+376174427616 x^{9}+677082445416 x^{10}+1015602174288 x^{11}+1269491970942 x^{12}+1318314865122 x^{13}+\frac {15819767221203}{14} x^{14}+790988281344 x^{15}+444930908256 x^{16}+196293047760 x^{17}+65431015920 x^{18}+15496819560 x^{19}+2324522934 x^{20}+\frac {1162261467}{7} x^{21}\) | \(105\) |
risch | \(1056832 x +15808800 x^{2}+149902032 x^{3}+1010576952 x^{4}+5149786572 x^{5}+20588764518 x^{6}+66158154783 x^{7}+173635132896 x^{8}+376174427616 x^{9}+677082445416 x^{10}+1015602174288 x^{11}+1269491970942 x^{12}+1318314865122 x^{13}+\frac {15819767221203}{14} x^{14}+790988281344 x^{15}+444930908256 x^{16}+196293047760 x^{17}+65431015920 x^{18}+15496819560 x^{19}+2324522934 x^{20}+\frac {1162261467}{7} x^{21}\) | \(105\) |
parallelrisch | \(1056832 x +15808800 x^{2}+149902032 x^{3}+1010576952 x^{4}+5149786572 x^{5}+20588764518 x^{6}+66158154783 x^{7}+173635132896 x^{8}+376174427616 x^{9}+677082445416 x^{10}+1015602174288 x^{11}+1269491970942 x^{12}+1318314865122 x^{13}+\frac {15819767221203}{14} x^{14}+790988281344 x^{15}+444930908256 x^{16}+196293047760 x^{17}+65431015920 x^{18}+15496819560 x^{19}+2324522934 x^{20}+\frac {1162261467}{7} x^{21}\) | \(105\) |
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Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (28) = 56\).
Time = 0.27 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.06 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1162261467}{7} \, x^{21} + 2324522934 \, x^{20} + 15496819560 \, x^{19} + 65431015920 \, x^{18} + 196293047760 \, x^{17} + 444930908256 \, x^{16} + 790988281344 \, x^{15} + \frac {15819767221203}{14} \, x^{14} + 1318314865122 \, x^{13} + 1269491970942 \, x^{12} + 1015602174288 \, x^{11} + 677082445416 \, x^{10} + 376174427616 \, x^{9} + 173635132896 \, x^{8} + 66158154783 \, x^{7} + 20588764518 \, x^{6} + 5149786572 \, x^{5} + 1010576952 \, x^{4} + 149902032 \, x^{3} + 15808800 \, x^{2} + 1056832 \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (24) = 48\).
Time = 0.04 (sec) , antiderivative size = 107, normalized size of antiderivative = 3.15 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1162261467 x^{21}}{7} + 2324522934 x^{20} + 15496819560 x^{19} + 65431015920 x^{18} + 196293047760 x^{17} + 444930908256 x^{16} + 790988281344 x^{15} + \frac {15819767221203 x^{14}}{14} + 1318314865122 x^{13} + 1269491970942 x^{12} + 1015602174288 x^{11} + 677082445416 x^{10} + 376174427616 x^{9} + 173635132896 x^{8} + 66158154783 x^{7} + 20588764518 x^{6} + 5149786572 x^{5} + 1010576952 x^{4} + 149902032 x^{3} + 15808800 x^{2} + 1056832 x \]
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Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (28) = 56\).
Time = 0.21 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.06 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1162261467}{7} \, x^{21} + 2324522934 \, x^{20} + 15496819560 \, x^{19} + 65431015920 \, x^{18} + 196293047760 \, x^{17} + 444930908256 \, x^{16} + 790988281344 \, x^{15} + \frac {15819767221203}{14} \, x^{14} + 1318314865122 \, x^{13} + 1269491970942 \, x^{12} + 1015602174288 \, x^{11} + 677082445416 \, x^{10} + 376174427616 \, x^{9} + 173635132896 \, x^{8} + 66158154783 \, x^{7} + 20588764518 \, x^{6} + 5149786572 \, x^{5} + 1010576952 \, x^{4} + 149902032 \, x^{3} + 15808800 \, x^{2} + 1056832 \, x \]
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Time = 0.35 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.82 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {1}{63} \, {\left (3 \, x + 2\right )}^{21} + \frac {1}{42} \, {\left (3 \, x + 2\right )}^{14} + \frac {1}{21} \, {\left (3 \, x + 2\right )}^{7} \]
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Time = 8.50 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.85 \[ \int (2+3 x)^6 \left (1+(2+3 x)^7+(2+3 x)^{14}\right ) \, dx=\frac {{\left (3\,x+2\right )}^7\,\left (3\,{\left (3\,x+2\right )}^7+2\,{\left (3\,x+2\right )}^{14}+6\right )}{126} \]
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