Optimal. Leaf size=23 \[ \text {Int}\left (\frac {e+f x}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2},x\right ) \]
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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 = {} \[ \int \frac {e+f x}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {e+f x}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2} \, dx &=\int \frac {e+f x}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2} \, dx\\ \end {align*}
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Mathematica [A] time = 19.40, size = 0, normalized size = 0.00 \[ \int \frac {e+f x}{\left (a+b \sin \left (c+\frac {d}{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.56, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {f x + e}{b^{2} \cos \left (\frac {c x + d}{x}\right )^{2} - 2 \, a b \sin \left (\frac {c x + d}{x}\right ) - a^{2} - b^{2}}, x\right ) \]
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 \[ \int \frac {f x + e}{{\left (b \sin \left (c + \frac {d}{x}\right ) + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.79, size = 0, normalized size = 0.00 \[ \int \frac {f x +e}{\left (a +b \sin \left (c +\frac {d}{x}\right )\right )^{2}}\, dx \]
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 \[ \text {result too large to display} \]
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 \[ \int \frac {e+f\,x}{{\left (a+b\,\sin \left (c+\frac {d}{x}\right )\right )}^2} \,d x \]
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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