Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x) (a+b \cot (e+f x))^2},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {1}{(c+d x) (a+b \cot (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(c+d x) (a+b \cot (e+f x))^2} \, dx &=\int \frac {1}{(c+d x) (a+b \cot (e+f x))^2} \, dx\\ \end {align*}
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Mathematica [A] time = 19.28, size = 0, normalized size = 0.00 \[ \int \frac {1}{(c+d x) (a+b \cot (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.67, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a^{2} d x + a^{2} c + {\left (b^{2} d x + b^{2} c\right )} \cot \left (f x + e\right )^{2} + 2 \, {\left (a b d x + a b c\right )} \cot \left (f x + e\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (d x + c\right )} {\left (b \cot \left (f x + e\right ) + a\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 13.35, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d x +c \right ) \left (a +b \cot \left (f x +e \right )\right )^{2}}\, dx \]
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 = -0.04 \[ \int \frac {1}{{\left (a+b\,\mathrm {cot}\left (e+f\,x\right )\right )}^2\,\left (c+d\,x\right )} \,d x \]
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 \[ \int \frac {1}{\left (a + b \cot {\left (e + f x \right )}\right )^{2} \left (c + d x\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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