Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )},x\right ) \]
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Rubi [A] time = 0.0274094, 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 = {} \[ \int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )} \, dx &=\int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.350616, size = 0, normalized size = 0. \[ \int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.04, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{3} \left ( a+b\sin \left ( d{x}^{2}+c \right ) \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}{{\left (b \sin \left (d x^{2} + c\right ) + a\right )} x^{3}}\,{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{1}{b x^{3} \sin \left (d x^{2} + c\right ) + a x^{3}}, 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^{3} \left (a + b \sin{\left (c + d x^{2} \right )}\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}{{\left (b \sin \left (d x^{2} + c\right ) + a\right )} x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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