Optimal. Leaf size=30 \[ \text{Unintegrable}\left (\frac{\sin ^3(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0691858, 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 = {} \[ \int \frac{\sin ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\sin ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx &=\int \frac{\sin ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx\\ \end{align*}
Mathematica [A] time = 5.84541, size = 0, normalized size = 0. \[ \int \frac{\sin ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.973, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \sin \left ( dx+c \right ) \right ) ^{3}}{ \left ( fx+e \right ) ^{2} \left ( a+a\sin \left ( dx+c \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{{\left (\cos \left (d x + c\right )^{2} - 1\right )} \sin \left (d x + c\right )}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} +{\left (a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right )} \sin \left (d x + c\right )}, 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{\sin \left (d x + c\right )^{3}}{{\left (f x + e\right )}^{2}{\left (a \sin \left (d x + c\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]