Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\cot ^2(a+b x)}{x},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {\cot ^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\cot ^2(a+b x)}{x} \, dx &=\int \frac {\cot ^2(a+b x)}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 3.82, size = 0, normalized size = 0.00 \[ \int \frac {\cot ^2(a+b x)}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 2.10, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cot \left (b x + a\right )^{2}}{x}, x\right ) \]
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 \[ \int \frac {\cot \left (b x + a\right )^{2}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.05, size = 0, normalized size = 0.00 \[ \int \frac {\cot ^{2}\left (b x +a \right )}{x}\, dx \]
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 \[ -\frac {b x \cos \left (2 \, b x + 2 \, a\right )^{2} \log \relax (x) + b x \log \relax (x) \sin \left (2 \, b x + 2 \, a\right )^{2} - 2 \, b x \cos \left (2 \, b x + 2 \, a\right ) \log \relax (x) + b x \log \relax (x) - \frac {{\left (b^{2} x \cos \left (2 \, b x + 2 \, a\right )^{2} + b^{2} x \sin \left (2 \, b x + 2 \, a\right )^{2} - 2 \, b^{2} x \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x\right )} \int \frac {\sin \left (b x + a\right )}{{\left (\cos \left (b x + a\right )^{2} + \sin \left (b x + a\right )^{2} + 2 \, \cos \left (b x + a\right ) + 1\right )} x^{2}}\,{d x}}{b^{2}} + \frac {{\left (b^{2} x \cos \left (2 \, b x + 2 \, a\right )^{2} + b^{2} x \sin \left (2 \, b x + 2 \, a\right )^{2} - 2 \, b^{2} x \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x\right )} \int \frac {\sin \left (b x + a\right )}{{\left (\cos \left (b x + a\right )^{2} + \sin \left (b x + a\right )^{2} - 2 \, \cos \left (b x + a\right ) + 1\right )} x^{2}}\,{d x}}{b^{2}} + 2 \, \sin \left (2 \, b x + 2 \, a\right )}{b x \cos \left (2 \, b x + 2 \, a\right )^{2} + b x \sin \left (2 \, b x + 2 \, a\right )^{2} - 2 \, b x \cos \left (2 \, b x + 2 \, a\right ) + b x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\mathrm {cot}\left (a+b\,x\right )}^2}{x} \,d x \]
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 \[ \int \frac {\cot ^{2}{\left (a + b x \right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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