Optimal. Leaf size=97 \[ \frac{256 x^{17}}{17}+\frac{1024 x^{15}}{15}+\frac{512 x^{14}}{7}+\frac{1792 x^{13}}{13}+256 x^{12}+\frac{3328 x^{11}}{11}+384 x^{10}+\frac{4192 x^9}{9}+448 x^8+\frac{2752 x^7}{7}+\frac{992 x^6}{3}+\frac{1136 x^5}{5}+112 x^4+\frac{112 x^3}{3}+8 x^2+x \]
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Rubi [A] time = 0.027978, antiderivative size = 97, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {2061} \[ \frac{256 x^{17}}{17}+\frac{1024 x^{15}}{15}+\frac{512 x^{14}}{7}+\frac{1792 x^{13}}{13}+256 x^{12}+\frac{3328 x^{11}}{11}+384 x^{10}+\frac{4192 x^9}{9}+448 x^8+\frac{2752 x^7}{7}+\frac{992 x^6}{3}+\frac{1136 x^5}{5}+112 x^4+\frac{112 x^3}{3}+8 x^2+x \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin{align*} \int \left (1+4 x+4 x^2+4 x^4\right )^4 \, dx &=\int \left (1+16 x+112 x^2+448 x^3+1136 x^4+1984 x^5+2752 x^6+3584 x^7+4192 x^8+3840 x^9+3328 x^{10}+3072 x^{11}+1792 x^{12}+1024 x^{13}+1024 x^{14}+256 x^{16}\right ) \, dx\\ &=x+8 x^2+\frac{112 x^3}{3}+112 x^4+\frac{1136 x^5}{5}+\frac{992 x^6}{3}+\frac{2752 x^7}{7}+448 x^8+\frac{4192 x^9}{9}+384 x^{10}+\frac{3328 x^{11}}{11}+256 x^{12}+\frac{1792 x^{13}}{13}+\frac{512 x^{14}}{7}+\frac{1024 x^{15}}{15}+\frac{256 x^{17}}{17}\\ \end{align*}
Mathematica [A] time = 0.0014482, size = 97, normalized size = 1. \[ \frac{256 x^{17}}{17}+\frac{1024 x^{15}}{15}+\frac{512 x^{14}}{7}+\frac{1792 x^{13}}{13}+256 x^{12}+\frac{3328 x^{11}}{11}+384 x^{10}+\frac{4192 x^9}{9}+448 x^8+\frac{2752 x^7}{7}+\frac{992 x^6}{3}+\frac{1136 x^5}{5}+112 x^4+\frac{112 x^3}{3}+8 x^2+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 78, normalized size = 0.8 \begin{align*} x+8\,{x}^{2}+{\frac{112\,{x}^{3}}{3}}+112\,{x}^{4}+{\frac{1136\,{x}^{5}}{5}}+{\frac{992\,{x}^{6}}{3}}+{\frac{2752\,{x}^{7}}{7}}+448\,{x}^{8}+{\frac{4192\,{x}^{9}}{9}}+384\,{x}^{10}+{\frac{3328\,{x}^{11}}{11}}+256\,{x}^{12}+{\frac{1792\,{x}^{13}}{13}}+{\frac{512\,{x}^{14}}{7}}+{\frac{1024\,{x}^{15}}{15}}+{\frac{256\,{x}^{17}}{17}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15065, size = 104, normalized size = 1.07 \begin{align*} \frac{256}{17} \, x^{17} + \frac{1024}{15} \, x^{15} + \frac{512}{7} \, x^{14} + \frac{1792}{13} \, x^{13} + 256 \, x^{12} + \frac{3328}{11} \, x^{11} + 384 \, x^{10} + \frac{4192}{9} \, x^{9} + 448 \, x^{8} + \frac{2752}{7} \, x^{7} + \frac{992}{3} \, x^{6} + \frac{1136}{5} \, x^{5} + 112 \, x^{4} + \frac{112}{3} \, x^{3} + 8 \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.11911, size = 254, normalized size = 2.62 \begin{align*} \frac{256}{17} x^{17} + \frac{1024}{15} x^{15} + \frac{512}{7} x^{14} + \frac{1792}{13} x^{13} + 256 x^{12} + \frac{3328}{11} x^{11} + 384 x^{10} + \frac{4192}{9} x^{9} + 448 x^{8} + \frac{2752}{7} x^{7} + \frac{992}{3} x^{6} + \frac{1136}{5} x^{5} + 112 x^{4} + \frac{112}{3} x^{3} + 8 x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067993, size = 94, normalized size = 0.97 \begin{align*} \frac{256 x^{17}}{17} + \frac{1024 x^{15}}{15} + \frac{512 x^{14}}{7} + \frac{1792 x^{13}}{13} + 256 x^{12} + \frac{3328 x^{11}}{11} + 384 x^{10} + \frac{4192 x^{9}}{9} + 448 x^{8} + \frac{2752 x^{7}}{7} + \frac{992 x^{6}}{3} + \frac{1136 x^{5}}{5} + 112 x^{4} + \frac{112 x^{3}}{3} + 8 x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11347, size = 104, normalized size = 1.07 \begin{align*} \frac{256}{17} \, x^{17} + \frac{1024}{15} \, x^{15} + \frac{512}{7} \, x^{14} + \frac{1792}{13} \, x^{13} + 256 \, x^{12} + \frac{3328}{11} \, x^{11} + 384 \, x^{10} + \frac{4192}{9} \, x^{9} + 448 \, x^{8} + \frac{2752}{7} \, x^{7} + \frac{992}{3} \, x^{6} + \frac{1136}{5} \, x^{5} + 112 \, x^{4} + \frac{112}{3} \, x^{3} + 8 \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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