Optimal. Leaf size=28 \[ \text {Int}\left (\frac {e^{x (a d+b c)+a c+b d x^2}}{x},x\right ) \]
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Rubi [A] time = 0.14, 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 = {} \[ \int \frac {e^{(a+b x) (c+d x)}}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {e^{(a+b x) (c+d x)}}{x} \, dx &=\int \frac {e^{a c+(b c+a d) x+b d x^2}}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.56, size = 0, normalized size = 0.00 \[ \int \frac {e^{(a+b x) (c+d x)}}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.39, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (b d x^{2} + a c + {\left (b c + a d\right )} x\right )}}{x}, x\right ) \]
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 \[ \int \frac {e^{\left ({\left (b x + a\right )} {\left (d x + c\right )}\right )}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{\left (b x +a \right ) \left (d x +c \right )}}{x}\, dx \]
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 \[ \int \frac {e^{\left ({\left (b x + a\right )} {\left (d x + c\right )}\right )}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\mathrm {e}}^{\left (a+b\,x\right )\,\left (c+d\,x\right )}}{x} \,d x \]
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 \[ e^{a c} \int \frac {e^{a d x} e^{b c x} e^{b d x^{2}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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