Optimal. Leaf size=23 \[ \text {Int}\left (\frac {e+f x}{a+b \sin \left (c+\frac {d}{x}\right )},x\right ) \]
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Rubi [A] time = 0.02, 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 = {} \[ \int \frac {e+f x}{a+b \sin \left (c+\frac {d}{x}\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {e+f x}{a+b \sin \left (c+\frac {d}{x}\right )} \, dx &=\int \frac {e+f x}{a+b \sin \left (c+\frac {d}{x}\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {e+f x}{a+b \sin \left (c+\frac {d}{x}\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.71, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {f x + e}{b \sin \left (\frac {c x + d}{x}\right ) + a}, x\right ) \]
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 \[ \int \frac {f x + e}{b \sin \left (c + \frac {d}{x}\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {f x +e}{a +b \sin \left (c +\frac {d}{x}\right )}\, dx \]
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 \[ \int \frac {f x + e}{b \sin \left (c + \frac {d}{x}\right ) + a}\,{d x} \]
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 \[ \int \frac {e+f\,x}{a+b\,\sin \left (c+\frac {d}{x}\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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