Optimal. Leaf size=37 \[ \frac{1}{15} (x+1)^{15}-\frac{3}{14} (x+1)^{14}+\frac{3}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.0162581, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {27, 43} \[ \frac{1}{15} (x+1)^{15}-\frac{3}{14} (x+1)^{14}+\frac{3}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin{align*} \int x^3 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^3 (1+x)^{11} \, dx\\ &=\int \left (-(1+x)^{11}+3 (1+x)^{12}-3 (1+x)^{13}+(1+x)^{14}\right ) \, dx\\ &=-\frac{1}{12} (1+x)^{12}+\frac{3}{13} (1+x)^{13}-\frac{3}{14} (1+x)^{14}+\frac{1}{15} (1+x)^{15}\\ \end{align*}
Mathematica [B] time = 0.0014113, size = 83, normalized size = 2.24 \[ \frac{x^{15}}{15}+\frac{11 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{55 x^{12}}{4}+30 x^{11}+\frac{231 x^{10}}{5}+\frac{154 x^9}{3}+\frac{165 x^8}{4}+\frac{165 x^7}{7}+\frac{55 x^6}{6}+\frac{11 x^5}{5}+\frac{x^4}{4} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 62, normalized size = 1.7 \begin{align*}{\frac{{x}^{15}}{15}}+{\frac{11\,{x}^{14}}{14}}+{\frac{55\,{x}^{13}}{13}}+{\frac{55\,{x}^{12}}{4}}+30\,{x}^{11}+{\frac{231\,{x}^{10}}{5}}+{\frac{154\,{x}^{9}}{3}}+{\frac{165\,{x}^{8}}{4}}+{\frac{165\,{x}^{7}}{7}}+{\frac{55\,{x}^{6}}{6}}+{\frac{11\,{x}^{5}}{5}}+{\frac{{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.00283, size = 82, normalized size = 2.22 \begin{align*} \frac{1}{15} \, x^{15} + \frac{11}{14} \, x^{14} + \frac{55}{13} \, x^{13} + \frac{55}{4} \, x^{12} + 30 \, x^{11} + \frac{231}{5} \, x^{10} + \frac{154}{3} \, x^{9} + \frac{165}{4} \, x^{8} + \frac{165}{7} \, x^{7} + \frac{55}{6} \, x^{6} + \frac{11}{5} \, x^{5} + \frac{1}{4} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.15406, size = 189, normalized size = 5.11 \begin{align*} \frac{1}{15} x^{15} + \frac{11}{14} x^{14} + \frac{55}{13} x^{13} + \frac{55}{4} x^{12} + 30 x^{11} + \frac{231}{5} x^{10} + \frac{154}{3} x^{9} + \frac{165}{4} x^{8} + \frac{165}{7} x^{7} + \frac{55}{6} x^{6} + \frac{11}{5} x^{5} + \frac{1}{4} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.078233, size = 75, normalized size = 2.03 \begin{align*} \frac{x^{15}}{15} + \frac{11 x^{14}}{14} + \frac{55 x^{13}}{13} + \frac{55 x^{12}}{4} + 30 x^{11} + \frac{231 x^{10}}{5} + \frac{154 x^{9}}{3} + \frac{165 x^{8}}{4} + \frac{165 x^{7}}{7} + \frac{55 x^{6}}{6} + \frac{11 x^{5}}{5} + \frac{x^{4}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11783, size = 82, normalized size = 2.22 \begin{align*} \frac{1}{15} \, x^{15} + \frac{11}{14} \, x^{14} + \frac{55}{13} \, x^{13} + \frac{55}{4} \, x^{12} + 30 \, x^{11} + \frac{231}{5} \, x^{10} + \frac{154}{3} \, x^{9} + \frac{165}{4} \, x^{8} + \frac{165}{7} \, x^{7} + \frac{55}{6} \, x^{6} + \frac{11}{5} \, x^{5} + \frac{1}{4} \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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