Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0275243, 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 = {} \[ \int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )^2} \, dx &=\int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 8.16858, size = 0, normalized size = 0. \[ \int \frac{1}{x^3 \left (a+b \sin \left (c+d x^2\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.921, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{{x}^{3} \left ( a+b\sin \left ( d{x}^{2}+c \right ) \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [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.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{1}{b^{2} x^{3} \cos \left (d x^{2} + c\right )^{2} - 2 \, a b x^{3} \sin \left (d x^{2} + c\right ) -{\left (a^{2} + b^{2}\right )} x^{3}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
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 )}^{2} x^{3}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]