3.203 \(\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx\)

Optimal. Leaf size=33 \[ \text{Unintegrable}\left (\frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right ) \]

[Out]

Unintegrable[Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0780933, 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 = {} \[ \int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]

[Out]

Defer[Int][Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]

Rubi steps

\begin{align*} \int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx &=\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx\\ \end{align*}

Mathematica [F]  time = 180.003, size = 0, normalized size = 0. \[ \text{\$Aborted} \]

Verification is Not applicable to the result.

[In]

Integrate[Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]

[Out]

$Aborted

________________________________________________________________________________________

Maple [A]  time = 0.137, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \sinh \left ( dx+c \right ) \right ) ^{3}}{ \left ( fx+e \right ) \left ( a+ia\sinh \left ( dx+c \right ) \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sinh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x)

[Out]

int(sinh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x)

________________________________________________________________________________________

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]

integrate(sinh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \frac{{\left (-i \, a d f x - i \, a d e +{\left (a d f x + a d e\right )} e^{\left (d x + c\right )}\right )}{\rm integral}\left (-\frac{d f x + d e -{\left (-i \, d f x - i \, d e\right )} e^{\left (5 \, d x + 5 \, c\right )} -{\left (d f x + d e\right )} e^{\left (4 \, d x + 4 \, c\right )} -{\left (4 i \, d f x + 4 i \, d e\right )} e^{\left (3 \, d x + 3 \, c\right )} - 4 \,{\left (d f x + d e + 2 \, f\right )} e^{\left (2 \, d x + 2 \, c\right )} -{\left (i \, d f x + i \, d e\right )} e^{\left (d x + c\right )}}{4 \,{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (3 \, d x + 3 \, c\right )} +{\left (-4 i \, a d f^{2} x^{2} - 8 i \, a d e f x - 4 i \, a d e^{2}\right )} e^{\left (2 \, d x + 2 \, c\right )}}, x\right ) + 2}{-i \, a d f x - i \, a d e +{\left (a d f x + a d e\right )} e^{\left (d x + c\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sinh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm="fricas")

[Out]

((-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))*integral(-(d*f*x + d*e - (-I*d*f*x - I*d*e)*e^(5*d*x +
5*c) - (d*f*x + d*e)*e^(4*d*x + 4*c) - (4*I*d*f*x + 4*I*d*e)*e^(3*d*x + 3*c) - 4*(d*f*x + d*e + 2*f)*e^(2*d*x
+ 2*c) - (I*d*f*x + I*d*e)*e^(d*x + c))/(4*(a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(3*d*x + 3*c) + (-4*I*a*d*
f^2*x^2 - 8*I*a*d*e*f*x - 4*I*a*d*e^2)*e^(2*d*x + 2*c)), x) + 2)/(-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(
d*x + c))

________________________________________________________________________________________

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]

integrate(sinh(d*x+c)**3/(f*x+e)/(a+I*a*sinh(d*x+c)),x)

[Out]

Timed out

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sinh \left (d x + c\right )^{3}}{{\left (f x + e\right )}{\left (i \, a \sinh \left (d x + c\right ) + a\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sinh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm="giac")

[Out]

integrate(sinh(d*x + c)^3/((f*x + e)*(I*a*sinh(d*x + c) + a)), x)