Optimal. Leaf size=55 \[ 8 x^4-140 e^{x^4}+490 e^{2 x^4}-\frac{3430 e^{3 x^4}}{3}+\frac{12005 e^{4 x^4}}{8}-\frac{16807 e^{5 x^4}}{20} \]
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Rubi [A] time = 0.0857752, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {6715, 2282, 43} \[ 8 x^4-140 e^{x^4}+490 e^{2 x^4}-\frac{3430 e^{3 x^4}}{3}+\frac{12005 e^{4 x^4}}{8}-\frac{16807 e^{5 x^4}}{20} \]
Antiderivative was successfully verified.
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Rule 6715
Rule 2282
Rule 43
Rubi steps
\begin{align*} \int \left (2-7 e^{x^4}\right )^5 x^3 \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \left (2-7 e^x\right )^5 \, dx,x,x^4\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \frac{(2-7 x)^5}{x} \, dx,x,e^{x^4}\right )\\ &=\frac{1}{4} \operatorname{Subst}\left (\int \left (-560+\frac{32}{x}+3920 x-13720 x^2+24010 x^3-16807 x^4\right ) \, dx,x,e^{x^4}\right )\\ &=-140 e^{x^4}+490 e^{2 x^4}-\frac{3430 e^{3 x^4}}{3}+\frac{12005 e^{4 x^4}}{8}-\frac{16807 e^{5 x^4}}{20}+8 x^4\\ \end{align*}
Mathematica [A] time = 0.0289462, size = 55, normalized size = 1. \[ 8 x^4-140 e^{x^4}+490 e^{2 x^4}-\frac{3430 e^{3 x^4}}{3}+\frac{12005 e^{4 x^4}}{8}-\frac{16807 e^{5 x^4}}{20} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.021, size = 47, normalized size = 0.9 \begin{align*} -{\frac{16807\, \left ({{\rm e}^{{x}^{4}}} \right ) ^{5}}{20}}+{\frac{12005\, \left ({{\rm e}^{{x}^{4}}} \right ) ^{4}}{8}}-{\frac{3430\, \left ({{\rm e}^{{x}^{4}}} \right ) ^{3}}{3}}+490\, \left ({{\rm e}^{{x}^{4}}} \right ) ^{2}-140\,{{\rm e}^{{x}^{4}}}+8\,\ln \left ({{\rm e}^{{x}^{4}}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.974356, size = 59, normalized size = 1.07 \begin{align*} 8 \, x^{4} - \frac{16807}{20} \, e^{\left (5 \, x^{4}\right )} + \frac{12005}{8} \, e^{\left (4 \, x^{4}\right )} - \frac{3430}{3} \, e^{\left (3 \, x^{4}\right )} + 490 \, e^{\left (2 \, x^{4}\right )} - 140 \, e^{\left (x^{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.925768, size = 131, normalized size = 2.38 \begin{align*} 8 \, x^{4} - \frac{16807}{20} \, e^{\left (5 \, x^{4}\right )} + \frac{12005}{8} \, e^{\left (4 \, x^{4}\right )} - \frac{3430}{3} \, e^{\left (3 \, x^{4}\right )} + 490 \, e^{\left (2 \, x^{4}\right )} - 140 \, e^{\left (x^{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.141958, size = 49, normalized size = 0.89 \begin{align*} 8 x^{4} - \frac{16807 e^{5 x^{4}}}{20} + \frac{12005 e^{4 x^{4}}}{8} - \frac{3430 e^{3 x^{4}}}{3} + 490 e^{2 x^{4}} - 140 e^{x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26594, size = 59, normalized size = 1.07 \begin{align*} 8 \, x^{4} - \frac{16807}{20} \, e^{\left (5 \, x^{4}\right )} + \frac{12005}{8} \, e^{\left (4 \, x^{4}\right )} - \frac{3430}{3} \, e^{\left (3 \, x^{4}\right )} + 490 \, e^{\left (2 \, x^{4}\right )} - 140 \, e^{\left (x^{4}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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