Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1}{x^2 \left (a+b e^{c+d x}\right )},x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx &=\int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b x^{2} e^{\left (d x + c\right )} + a x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (b \,{\mathrm e}^{d x +c}+a \right ) x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b e^{\left (d x + c\right )} + a\right )} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x^2\,\left (a+b\,{\mathrm {e}}^{c+d\,x}\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \left (a + b e^{c} e^{d x}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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