Optimal. Leaf size=18 \[ \text {Int}\left (\frac {\tan ^{-1}(d \cot (a+b x)+c)}{x},x\right ) \]
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Rubi [A] time = 0.13, 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 = {} \[ \int \frac {\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx &=\int \frac {\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 5.13, size = 0, normalized size = 0.00 \[ \int \frac {\tan ^{-1}(c+d \cot (a+b x))}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\arctan \left (d \cot \left (b x + a\right ) + c\right )}{x}, x\right ) \]
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 \[ \int \frac {\arctan \left (d \cot \left (b x + a\right ) + c\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.30, size = 0, normalized size = 0.00 \[ \int \frac {\arctan \left (c +d \cot \left (b x +a \right )\right )}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [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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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {\mathrm {atan}\left (c+d\,\mathrm {cot}\left (a+b\,x\right )\right )}{x} \,d x \]
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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