Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{x^2 \left (a+b \tan \left (c+d \sqrt{x}\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0260402, 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 = {} \[ \int \frac{1}{x^2 \left (a+b \tan \left (c+d \sqrt{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x^2 \left (a+b \tan \left (c+d \sqrt{x}\right )\right )^2} \, dx &=\int \frac{1}{x^2 \left (a+b \tan \left (c+d \sqrt{x}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 18.2554, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \left (a+b \tan \left (c+d \sqrt{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.268, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2}} \left ( a+b\tan \left ( c+d\sqrt{x} \right ) \right ) ^{-2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: RuntimeError} \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{1}{b^{2} x^{2} \tan \left (d \sqrt{x} + c\right )^{2} + 2 \, a b x^{2} \tan \left (d \sqrt{x} + c\right ) + a^{2} x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{1}{{\left (b \tan \left (d \sqrt{x} + c\right ) + a\right )}^{2} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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