Optimal. Leaf size=26 \[ 5 e^4 \left (e^{4 x-\left (\frac {75}{x^2}+x\right )^2}+2 x\right ) \]
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Rubi [A] time = 0.33, antiderivative size = 31, normalized size of antiderivative = 1.19, number of steps used = 3, number of rules used = 2, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {14, 6706} \begin {gather*} 5 e^{-\frac {5625}{x^4}-x^2+4 x-\frac {150}{x}+4}+10 e^4 x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (10 e^4-\frac {10 e^{4-\frac {5625}{x^4}-\frac {150}{x}+4 x-x^2} \left (-11250-75 x^3-2 x^5+x^6\right )}{x^5}\right ) \, dx\\ &=10 e^4 x-10 \int \frac {e^{4-\frac {5625}{x^4}-\frac {150}{x}+4 x-x^2} \left (-11250-75 x^3-2 x^5+x^6\right )}{x^5} \, dx\\ &=5 e^{4-\frac {5625}{x^4}-\frac {150}{x}+4 x-x^2}+10 e^4 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.21, size = 31, normalized size = 1.19 \begin {gather*} e^4 \left (5 e^{-\frac {5625}{x^4}-\frac {150}{x}+4 x-x^2}+10 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 34, normalized size = 1.31 \begin {gather*} 10 \, x e^{4} + 5 \, e^{\left (-\frac {x^{6} - 4 \, x^{5} - 4 \, x^{4} + 150 \, x^{3} + 5625}{x^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 34, normalized size = 1.31 \begin {gather*} 10 \, x e^{4} + 5 \, e^{\left (-\frac {x^{6} - 4 \, x^{5} - 4 \, x^{4} + 150 \, x^{3} + 5625}{x^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.62, size = 35, normalized size = 1.35
method | result | size |
risch | \(10 x \,{\mathrm e}^{4}+5 \,{\mathrm e}^{-\frac {x^{6}-4 x^{5}-4 x^{4}+150 x^{3}+5625}{x^{4}}}\) | \(35\) |
norman | \(\frac {10 x^{5} {\mathrm e}^{4}+5 x^{4} {\mathrm e}^{4} {\mathrm e}^{\frac {-x^{6}+4 x^{5}-150 x^{3}-5625}{x^{4}}}}{x^{4}}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 29, normalized size = 1.12 \begin {gather*} 10 \, x e^{4} + 5 \, e^{\left (-x^{2} + 4 \, x - \frac {150}{x} - \frac {5625}{x^{4}} + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.23, size = 32, normalized size = 1.23 \begin {gather*} 10\,x\,{\mathrm {e}}^4+5\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{-\frac {150}{x}}\,{\mathrm {e}}^{-\frac {5625}{x^4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 31, normalized size = 1.19 \begin {gather*} 10 x e^{4} + 5 e^{4} e^{\frac {- x^{6} + 4 x^{5} - 150 x^{3} - 5625}{x^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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