Optimal. Leaf size=21 \[ \frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
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Rubi [A] time = 0.0313831, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.103, Rules used = {1584, 446, 74} \[ \frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
Antiderivative was successfully verified.
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Rule 1584
Rule 446
Rule 74
Rubi steps
\begin{align*} \int x^{14 (-1+n)} \left (b+2 c x^n\right ) \left (b x+c x^{1+n}\right )^{13} \, dx &=\int x^{13+14 (-1+n)} \left (b+c x^n\right )^{13} \left (b+2 c x^n\right ) \, dx\\ &=\frac{\operatorname{Subst}\left (\int x^{13} (b+c x)^{13} (b+2 c x) \, dx,x,x^n\right )}{n}\\ &=\frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n}\\ \end{align*}
Mathematica [A] time = 0.115378, size = 21, normalized size = 1. \[ \frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.038, size = 230, normalized size = 11. \begin{align*}{\frac{{c}^{14} \left ({x}^{n} \right ) ^{28}}{14\,n}}+{\frac{b{c}^{13} \left ({x}^{n} \right ) ^{27}}{n}}+{\frac{13\,{c}^{12} \left ({x}^{n} \right ) ^{26}{b}^{2}}{2\,n}}+26\,{\frac{{b}^{3}{c}^{11} \left ({x}^{n} \right ) ^{25}}{n}}+{\frac{143\,{c}^{10} \left ({x}^{n} \right ) ^{24}{b}^{4}}{2\,n}}+143\,{\frac{{b}^{5}{c}^{9} \left ({x}^{n} \right ) ^{23}}{n}}+{\frac{429\,{c}^{8} \left ({x}^{n} \right ) ^{22}{b}^{6}}{2\,n}}+{\frac{1716\,{b}^{7}{c}^{7} \left ({x}^{n} \right ) ^{21}}{7\,n}}+{\frac{429\,{c}^{6} \left ({x}^{n} \right ) ^{20}{b}^{8}}{2\,n}}+143\,{\frac{{b}^{9}{c}^{5} \left ({x}^{n} \right ) ^{19}}{n}}+{\frac{143\,{c}^{4} \left ({x}^{n} \right ) ^{18}{b}^{10}}{2\,n}}+26\,{\frac{{b}^{11}{c}^{3} \left ({x}^{n} \right ) ^{17}}{n}}+{\frac{13\,{c}^{2} \left ({x}^{n} \right ) ^{16}{b}^{12}}{2\,n}}+{\frac{{b}^{13}c \left ({x}^{n} \right ) ^{15}}{n}}+{\frac{ \left ({x}^{n} \right ) ^{14}{b}^{14}}{14\,n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.61473, size = 657, normalized size = 31.29 \begin{align*} \frac{b^{14} x^{14} x^{14 \, n + 14} + 14 \, b^{13} c x^{13} x^{15 \, n + 15} + 91 \, b^{12} c^{2} x^{12} x^{16 \, n + 16} + 364 \, b^{11} c^{3} x^{11} x^{17 \, n + 17} + 1001 \, b^{10} c^{4} x^{10} x^{18 \, n + 18} + 2002 \, b^{9} c^{5} x^{9} x^{19 \, n + 19} + 3003 \, b^{8} c^{6} x^{8} x^{20 \, n + 20} + 3432 \, b^{7} c^{7} x^{7} x^{21 \, n + 21} + 3003 \, b^{6} c^{8} x^{6} x^{22 \, n + 22} + 2002 \, b^{5} c^{9} x^{5} x^{23 \, n + 23} + 1001 \, b^{4} c^{10} x^{4} x^{24 \, n + 24} + 364 \, b^{3} c^{11} x^{3} x^{25 \, n + 25} + 91 \, b^{2} c^{12} x^{2} x^{26 \, n + 26} + 14 \, b c^{13} x x^{27 \, n + 27} + c^{14} x^{28 \, n + 28}}{14 \, n x^{28}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.86753, size = 255, normalized size = 12.14 \begin{align*} \frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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