Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{\tan ^3(a+b x)}{x^2},x\right ) \]
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Rubi [A] time = 0.0277722, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\tan ^3(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\tan ^3(a+b x)}{x^2} \, dx &=\int \frac{\tan ^3(a+b x)}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 3.16353, size = 0, normalized size = 0. \[ \int \frac{\tan ^3(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.722, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \tan \left ( bx+a \right ) \right ) ^{3}}{{x}^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{4 \, b x \cos \left (2 \, b x + 2 \, a\right )^{2} + 4 \, b x \sin \left (2 \, b x + 2 \, a\right )^{2} + 2 \, b x \cos \left (2 \, b x + 2 \, a\right ) + 2 \,{\left (b x \cos \left (2 \, b x + 2 \, a\right ) - \sin \left (2 \, b x + 2 \, a\right )\right )} \cos \left (4 \, b x + 4 \, a\right ) - 2 \,{\left (b^{2} x^{3} \cos \left (4 \, b x + 4 \, a\right )^{2} + 4 \, b^{2} x^{3} \cos \left (2 \, b x + 2 \, a\right )^{2} + b^{2} x^{3} \sin \left (4 \, b x + 4 \, a\right )^{2} + 4 \, b^{2} x^{3} \sin \left (4 \, b x + 4 \, a\right ) \sin \left (2 \, b x + 2 \, a\right ) + 4 \, b^{2} x^{3} \sin \left (2 \, b x + 2 \, a\right )^{2} + 4 \, b^{2} x^{3} \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x^{3} + 2 \,{\left (2 \, b^{2} x^{3} \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x^{3}\right )} \cos \left (4 \, b x + 4 \, a\right )\right )} \int \frac{{\left (b^{2} x^{2} - 3\right )} \sin \left (2 \, b x + 2 \, a\right )}{b^{2} x^{4} \cos \left (2 \, b x + 2 \, a\right )^{2} + b^{2} x^{4} \sin \left (2 \, b x + 2 \, a\right )^{2} + 2 \, b^{2} x^{4} \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x^{4}}\,{d x} + 2 \,{\left (b x \sin \left (2 \, b x + 2 \, a\right ) + \cos \left (2 \, b x + 2 \, a\right ) + 1\right )} \sin \left (4 \, b x + 4 \, a\right ) + 2 \, \sin \left (2 \, b x + 2 \, a\right )}{b^{2} x^{3} \cos \left (4 \, b x + 4 \, a\right )^{2} + 4 \, b^{2} x^{3} \cos \left (2 \, b x + 2 \, a\right )^{2} + b^{2} x^{3} \sin \left (4 \, b x + 4 \, a\right )^{2} + 4 \, b^{2} x^{3} \sin \left (4 \, b x + 4 \, a\right ) \sin \left (2 \, b x + 2 \, a\right ) + 4 \, b^{2} x^{3} \sin \left (2 \, b x + 2 \, a\right )^{2} + 4 \, b^{2} x^{3} \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x^{3} + 2 \,{\left (2 \, b^{2} x^{3} \cos \left (2 \, b x + 2 \, a\right ) + b^{2} x^{3}\right )} \cos \left (4 \, b x + 4 \, a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\tan \left (b x + a\right )^{3}}{x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\tan ^{3}{\left (a + b x \right )}}{x^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\tan \left (b x + a\right )^{3}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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