Optimal. Leaf size=82 \[ d \text{CannotIntegrate}\left (\frac{1}{(f+g x)^2 \left (a+b e^{h+i x}+c e^{2 h+2 i x}\right )},x\right )+e \text{CannotIntegrate}\left (\frac{e^{h+i x}}{(f+g x)^2 \left (a+b e^{h+i x}+c e^{2 h+2 i x}\right )},x\right ) \]
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Rubi [A] time = 0.869854, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{d+e e^{h+i x}}{\left (a+b e^{h+i x}+c e^{2 h+2 i x}\right ) (f+g x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{d+e e^{h+577 x}}{\left (a+b e^{h+577 x}+c e^{2 h+1154 x}\right ) (f+g x)^2} \, dx &=\int \left (\frac{d}{\left (a+b e^{h+577 x}+c e^{2 h+1154 x}\right ) (f+g x)^2}+\frac{e e^{h+577 x}}{\left (a+b e^{h+577 x}+c e^{2 h+1154 x}\right ) (f+g x)^2}\right ) \, dx\\ &=d \int \frac{1}{\left (a+b e^{h+577 x}+c e^{2 h+1154 x}\right ) (f+g x)^2} \, dx+e \int \frac{e^{h+577 x}}{\left (a+b e^{h+577 x}+c e^{2 h+1154 x}\right ) (f+g x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 5.76063, size = 0, normalized size = 0. \[ \int \frac{d+e e^{h+i x}}{\left (a+b e^{h+i x}+c e^{2 h+2 i x}\right ) (f+g x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.197, size = 0, normalized size = 0. \begin{align*} \int{\frac{d+e{{\rm e}^{ix+h}}}{ \left ( a+b{{\rm e}^{ix+h}}+c{{\rm e}^{2\,ix+2\,h}} \right ) \left ( gx+f \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e e^{\left (i x + h\right )} + d}{{\left (g x + f\right )}^{2}{\left (c e^{\left (2 \, i x + 2 \, h\right )} + b e^{\left (i x + h\right )} + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{e e^{\left (i x + h\right )} + d}{a g^{2} x^{2} + 2 \, a f g x + a f^{2} +{\left (c g^{2} x^{2} + 2 \, c f g x + c f^{2}\right )} e^{\left (2 \, i x + 2 \, h\right )} +{\left (b g^{2} x^{2} + 2 \, b f g x + b f^{2}\right )} e^{\left (i x + h\right )}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e e^{\left (i x + h\right )} + d}{{\left (g x + f\right )}^{2}{\left (c e^{\left (2 \, i x + 2 \, h\right )} + b e^{\left (i x + h\right )} + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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