Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x^2 \sqrt{a \sin (c+d x)+a}},x\right ) \]
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Rubi [A] time = 0.0735011, 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 = {} \[ \int \frac{1}{x^2 \sqrt{a+a \sin (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x^2 \sqrt{a+a \sin (c+d x)}} \, dx &=\int \frac{1}{x^2 \sqrt{a+a \sin (c+d x)}} \, dx\\ \end{align*}
Mathematica [A] time = 0.747242, size = 0, normalized size = 0. \[ \int \frac{1}{x^2 \sqrt{a+a \sin (c+d x)}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.049, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{2}}{\frac{1}{\sqrt{a+a\sin \left ( dx+c \right ) }}}}\, 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*} \int \frac{1}{\sqrt{a \sin \left (d x + c\right ) + a} x^{2}}\,{d x} \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{\sqrt{a \sin \left (d x + c\right ) + a}}{a x^{2} \sin \left (d x + c\right ) + a 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{1}{x^{2} \sqrt{a \left (\sin{\left (c + d x \right )} + 1\right )}}\, 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{1}{\sqrt{a \sin \left (d x + c\right ) + a} x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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