Optimal. Leaf size=22 \[ \frac {15}{4} e^{-\frac {2 x^4}{\left (x+(5+2 x)^2\right )^2}} \]
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Rubi [A] time = 0.69, antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 4, number of rules used = 4, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {1593, 6688, 12, 6706} \begin {gather*} \frac {15}{4} e^{-\frac {2 x^4}{\left (4 x^2+21 x+25\right )^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1593
Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-\frac {2 x^4}{625+1050 x+641 x^2+168 x^3+16 x^4}} (-750-315 x) x^3}{15625+39375 x+40575 x^2+21861 x^3+6492 x^4+1008 x^5+64 x^6} \, dx\\ &=\int \frac {15 e^{-\frac {2 x^4}{\left (25+21 x+4 x^2\right )^2}} (-50-21 x) x^3}{\left (25+21 x+4 x^2\right )^3} \, dx\\ &=15 \int \frac {e^{-\frac {2 x^4}{\left (25+21 x+4 x^2\right )^2}} (-50-21 x) x^3}{\left (25+21 x+4 x^2\right )^3} \, dx\\ &=\frac {15}{4} e^{-\frac {2 x^4}{\left (25+21 x+4 x^2\right )^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.52, size = 23, normalized size = 1.05 \begin {gather*} \frac {15}{4} e^{-\frac {2 x^4}{\left (25+21 x+4 x^2\right )^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 30, normalized size = 1.36 \begin {gather*} \frac {15}{4} \, e^{\left (-\frac {2 \, x^{4}}{16 \, x^{4} + 168 \, x^{3} + 641 \, x^{2} + 1050 \, x + 625}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 30, normalized size = 1.36 \begin {gather*} \frac {15}{4} \, e^{\left (-\frac {2 \, x^{4}}{16 \, x^{4} + 168 \, x^{3} + 641 \, x^{2} + 1050 \, x + 625}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 21, normalized size = 0.95
method | result | size |
risch | \(\frac {15 \,{\mathrm e}^{-\frac {2 x^{4}}{\left (4 x^{2}+21 x +25\right )^{2}}}}{4}\) | \(21\) |
gosper | \(\frac {15 \,{\mathrm e}^{-\frac {2 x^{4}}{16 x^{4}+168 x^{3}+641 x^{2}+1050 x +625}}}{4}\) | \(32\) |
norman | \(\frac {\left (\frac {9375}{4}+\frac {7875}{2} x +\frac {9615}{4} x^{2}+630 x^{3}+60 x^{4}\right ) {\mathrm e}^{-\frac {2 x^{4}}{16 x^{4}+168 x^{3}+641 x^{2}+1050 x +625}}}{\left (4 x^{2}+21 x +25\right )^{2}}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 4.99, size = 83, normalized size = 3.77 \begin {gather*} \frac {15}{4} \, e^{\left (\frac {5061 \, x}{32 \, {\left (16 \, x^{4} + 168 \, x^{3} + 641 \, x^{2} + 1050 \, x + 625\right )}} + \frac {21 \, x}{4 \, {\left (4 \, x^{2} + 21 \, x + 25\right )}} + \frac {8525}{32 \, {\left (16 \, x^{4} + 168 \, x^{3} + 641 \, x^{2} + 1050 \, x + 625\right )}} - \frac {241}{32 \, {\left (4 \, x^{2} + 21 \, x + 25\right )}} - \frac {1}{8}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.36, size = 30, normalized size = 1.36 \begin {gather*} \frac {15\,{\mathrm {e}}^{-\frac {2\,x^4}{16\,x^4+168\,x^3+641\,x^2+1050\,x+625}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 29, normalized size = 1.32 \begin {gather*} \frac {15 e^{- \frac {2 x^{4}}{16 x^{4} + 168 x^{3} + 641 x^{2} + 1050 x + 625}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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