Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0597691, 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 = {} \[ \int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx &=\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx\\ \end{align*}
Mathematica [A] time = 21.0866, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.164, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) ^{2} \left ( a+ia\sinh \left ( fx+e \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} 4 i \, d \int \frac{1}{-i \, a d^{3} f x^{3} - 3 i \, a c d^{2} f x^{2} - 3 i \, a c^{2} d f x - i \, a c^{3} f +{\left (a d^{3} f x^{3} e^{e} + 3 \, a c d^{2} f x^{2} e^{e} + 3 \, a c^{2} d f x e^{e} + a c^{3} f e^{e}\right )} e^{\left (f x\right )}}\,{d x} + \frac{2 i}{-i \, a d^{2} f x^{2} - 2 i \, a c d f x - i \, a c^{2} f +{\left (a d^{2} f x^{2} e^{e} + 2 \, a c d f x e^{e} + a c^{2} f e^{e}\right )} e^{\left (f x\right )}} \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*} \frac{{\left (-i \, a d^{2} f x^{2} - 2 i \, a c d f x - i \, a c^{2} f +{\left (a d^{2} f x^{2} + 2 \, a c d f x + a c^{2} f\right )} e^{\left (f x + e\right )}\right )}{\rm integral}\left (\frac{4 i \, d}{-i \, a d^{3} f x^{3} - 3 i \, a c d^{2} f x^{2} - 3 i \, a c^{2} d f x - i \, a c^{3} f +{\left (a d^{3} f x^{3} + 3 \, a c d^{2} f x^{2} + 3 \, a c^{2} d f x + a c^{3} f\right )} e^{\left (f x + e\right )}}, x\right ) + 2 i}{-i \, a d^{2} f x^{2} - 2 i \, a c d f x - i \, a c^{2} f +{\left (a d^{2} f x^{2} + 2 \, a c d f x + a c^{2} f\right )} e^{\left (f x + e\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 (d x + c\right )}^{2}{\left (i \, a \sinh \left (f x + e\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]