Optimal. Leaf size=22 \[ -e^{e^x+3 x}+\frac {25}{(-2+x) x} \]
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Rubi [A] time = 0.86, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 15, number of rules used = 8, integrand size = 68, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {1594, 27, 6688, 6742, 2282, 2176, 2194, 74} \begin {gather*} -e^{3 x+e^x}-\frac {25}{(2-x) x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 74
Rule 1594
Rule 2176
Rule 2194
Rule 2282
Rule 6688
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {50-50 x+e^{e^x+3 x} \left (-12 x^2+12 x^3-3 x^4+e^x \left (-4 x^2+4 x^3-x^4\right )\right )}{x^2 \left (4-4 x+x^2\right )} \, dx\\ &=\int \frac {50-50 x+e^{e^x+3 x} \left (-12 x^2+12 x^3-3 x^4+e^x \left (-4 x^2+4 x^3-x^4\right )\right )}{(-2+x)^2 x^2} \, dx\\ &=\int \frac {50-50 x-e^{e^x+3 x} \left (3+e^x\right ) (-2+x)^2 x^2}{(2-x)^2 x^2} \, dx\\ &=\int \left (-3 e^{e^x+3 x}-e^{e^x+4 x}-\frac {50 (-1+x)}{(-2+x)^2 x^2}\right ) \, dx\\ &=-\left (3 \int e^{e^x+3 x} \, dx\right )-50 \int \frac {-1+x}{(-2+x)^2 x^2} \, dx-\int e^{e^x+4 x} \, dx\\ &=-\frac {25}{(2-x) x}-3 \operatorname {Subst}\left (\int e^x x^2 \, dx,x,e^x\right )-\operatorname {Subst}\left (\int e^x x^3 \, dx,x,e^x\right )\\ &=-3 e^{e^x+2 x}-e^{e^x+3 x}-\frac {25}{(2-x) x}+3 \operatorname {Subst}\left (\int e^x x^2 \, dx,x,e^x\right )+6 \operatorname {Subst}\left (\int e^x x \, dx,x,e^x\right )\\ &=6 e^{e^x+x}-e^{e^x+3 x}-\frac {25}{(2-x) x}-6 \operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )-6 \operatorname {Subst}\left (\int e^x x \, dx,x,e^x\right )\\ &=-6 e^{e^x}-e^{e^x+3 x}-\frac {25}{(2-x) x}+6 \operatorname {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=-e^{e^x+3 x}-\frac {25}{(2-x) x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 22, normalized size = 1.00 \begin {gather*} -e^{e^x+3 x}+\frac {25}{(-2+x) x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 28, normalized size = 1.27 \begin {gather*} -\frac {{\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x + e^{x}\right )} - 25}{x^{2} - 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 48, normalized size = 2.18 \begin {gather*} -\frac {x^{2} e^{\left (7 \, x + e^{x}\right )} - 2 \, x e^{\left (7 \, x + e^{x}\right )} - 25 \, e^{\left (4 \, x\right )}}{x^{2} e^{\left (4 \, x\right )} - 2 \, x e^{\left (4 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 21, normalized size = 0.95
method | result | size |
risch | \(\frac {25}{\left (x -2\right ) x}-{\mathrm e}^{3 x +{\mathrm e}^{x}}\) | \(21\) |
norman | \(\frac {25+2 x \,{\mathrm e}^{3 x +{\mathrm e}^{x}}-{\mathrm e}^{3 x +{\mathrm e}^{x}} x^{2}}{\left (x -2\right ) x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 31, normalized size = 1.41 \begin {gather*} -\frac {25 \, {\left (x - 1\right )}}{x^{2} - 2 \, x} + \frac {25}{x - 2} - e^{\left (3 \, x + e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 23, normalized size = 1.05 \begin {gather*} -{\mathrm {e}}^{3\,x+{\mathrm {e}}^x}-\frac {25}{2\,x-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 15, normalized size = 0.68 \begin {gather*} - e^{3 x + e^{x}} + \frac {25}{x^{2} - 2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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