Optimal. Leaf size=22 \[ \text {Int}\left (\frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx &=\int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx\\ \end {align*}
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Mathematica [A] time = 1.27, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {c+d x}}{\left (a+b e^x\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {d x + c}}{b^{2} e^{\left (2 \, x\right )} + 2 \, a b e^{x} + a^{2}}, x\right ) \]
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 \[ \int \frac {\sqrt {d x + c}}{{\left (b e^{x} + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\sqrt {d x +c}}{\left (b \,{\mathrm e}^{x}+a \right )^{2}}\, dx \]
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 \[ \int \frac {\sqrt {d x + c}}{{\left (b e^{x} + a\right )}^{2}}\,{d x} \]
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 \[ \int \frac {\sqrt {c+d\,x}}{{\left (a+b\,{\mathrm {e}}^x\right )}^2} \,d x \]
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 \[ \int \frac {\sqrt {c + d x}}{\left (a + b e^{x}\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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