Optimal. Leaf size=24 \[ \frac {-2+e^{x^2}+x}{5+e^{5+e^{36 x^4}}} \]
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Rubi [F] time = 3.67, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {5+10 e^{x^2} x+e^{5+e^{36 x^4}} \left (1+2 e^{x^2} x+e^{36 x^4} \left (288 x^3-144 e^{x^2} x^3-144 x^4\right )\right )}{25+10 e^{5+e^{36 x^4}}+e^{10+2 e^{36 x^4}}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5+10 e^{x^2} x+e^{5+e^{36 x^4}} \left (1+2 e^{x^2} x-144 e^{36 x^4} x^3 \left (-2+e^{x^2}+x\right )\right )}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx\\ &=\int \left (\frac {5}{\left (5+e^{5+e^{36 x^4}}\right )^2}+\frac {e^{5+e^{36 x^4}}}{\left (5+e^{5+e^{36 x^4}}\right )^2}+\frac {10 e^{x^2} x}{\left (5+e^{5+e^{36 x^4}}\right )^2}+\frac {2 e^{5+e^{36 x^4}+x^2} x}{\left (5+e^{5+e^{36 x^4}}\right )^2}-\frac {144 e^{5+e^{36 x^4}+36 x^4} x^3 \left (-2+e^{x^2}+x\right )}{\left (5+e^{5+e^{36 x^4}}\right )^2}\right ) \, dx\\ &=2 \int \frac {e^{5+e^{36 x^4}+x^2} x}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+5 \int \frac {1}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+10 \int \frac {e^{x^2} x}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx-144 \int \frac {e^{5+e^{36 x^4}+36 x^4} x^3 \left (-2+e^{x^2}+x\right )}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+\int \frac {e^{5+e^{36 x^4}}}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx\\ &=5 \int \frac {1}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+5 \operatorname {Subst}\left (\int \frac {e^x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-144 \int \left (\frac {e^{5+e^{36 x^4}+x^2+36 x^4} x^3}{\left (5+e^{5+e^{36 x^4}}\right )^2}+\frac {e^{5+e^{36 x^4}+36 x^4} (-2+x) x^3}{\left (5+e^{5+e^{36 x^4}}\right )^2}\right ) \, dx+\int \left (-\frac {5}{\left (5+e^{5+e^{36 x^4}}\right )^2}+\frac {1}{5+e^{5+e^{36 x^4}}}\right ) \, dx+\operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x}}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )\\ &=5 \operatorname {Subst}\left (\int \frac {e^x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-144 \int \frac {e^{5+e^{36 x^4}+x^2+36 x^4} x^3}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx-144 \int \frac {e^{5+e^{36 x^4}+36 x^4} (-2+x) x^3}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+\int \frac {1}{5+e^{5+e^{36 x^4}}} \, dx+\operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x}}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )\\ &=5 \operatorname {Subst}\left (\int \frac {e^x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-72 \operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x+36 x^2} x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-144 \int \left (-\frac {2 e^{5+e^{36 x^4}+36 x^4} x^3}{\left (5+e^{5+e^{36 x^4}}\right )^2}+\frac {e^{5+e^{36 x^4}+36 x^4} x^4}{\left (5+e^{5+e^{36 x^4}}\right )^2}\right ) \, dx+\int \frac {1}{5+e^{5+e^{36 x^4}}} \, dx+\operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x}}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )\\ &=5 \operatorname {Subst}\left (\int \frac {e^x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-72 \operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x+36 x^2} x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-144 \int \frac {e^{5+e^{36 x^4}+36 x^4} x^4}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+288 \int \frac {e^{5+e^{36 x^4}+36 x^4} x^3}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+\int \frac {1}{5+e^{5+e^{36 x^4}}} \, dx+\operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x}}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )\\ &=-\frac {2}{5+e^{5+e^{36 x^4}}}+5 \operatorname {Subst}\left (\int \frac {e^x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-72 \operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x+36 x^2} x}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )-144 \int \frac {e^{5+e^{36 x^4}+36 x^4} x^4}{\left (5+e^{5+e^{36 x^4}}\right )^2} \, dx+\int \frac {1}{5+e^{5+e^{36 x^4}}} \, dx+\operatorname {Subst}\left (\int \frac {e^{5+e^{36 x^2}+x}}{\left (5+e^{5+e^{36 x^2}}\right )^2} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.71, size = 24, normalized size = 1.00 \begin {gather*} \frac {-2+e^{x^2}+x}{5+e^{5+e^{36 x^4}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 21, normalized size = 0.88 \begin {gather*} \frac {x + e^{\left (x^{2}\right )} - 2}{e^{\left (e^{\left (36 \, x^{4}\right )} + 5\right )} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 21, normalized size = 0.88 \begin {gather*} \frac {x + e^{\left (x^{2}\right )} - 2}{e^{\left (e^{\left (36 \, x^{4}\right )} + 5\right )} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 0.92
method | result | size |
risch | \(\frac {x -2+{\mathrm e}^{x^{2}}}{5+{\mathrm e}^{{\mathrm e}^{36 x^{4}}+5}}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 21, normalized size = 0.88 \begin {gather*} \frac {x + e^{\left (x^{2}\right )} - 2}{e^{\left (e^{\left (36 \, x^{4}\right )} + 5\right )} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.05, size = 59, normalized size = 2.46 \begin {gather*} \frac {{\mathrm {e}}^{-36\,x^4}\,\left (x^3\,{\mathrm {e}}^{36\,x^4+x^2}-2\,x^3\,{\mathrm {e}}^{36\,x^4}+x^4\,{\mathrm {e}}^{36\,x^4}\right )}{x^3\,\left ({\mathrm {e}}^{{\mathrm {e}}^{36\,x^4}+5}+5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 19, normalized size = 0.79 \begin {gather*} \frac {x + e^{x^{2}} - 2}{e^{e^{36 x^{4}} + 5} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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