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

Optimal. Leaf size=25 \[ \text{Unintegrable}\left (\frac{(c+d x)^m}{a+i a \sinh (e+f x)},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0561594, 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 = {} \[ \int \frac{(c+d x)^m}{a+i a \sinh (e+f x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 4.27846, size = 0, normalized size = 0. \[ \int \frac{(c+d x)^m}{a+i a \sinh (e+f x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.034, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( dx+c \right ) ^{m}}{a+ia\sinh \left ( fx+e \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((a*f*e^(f*x + e) - I*a*f)*integral(-2*I*(d*x + c)^m*d*m/(-I*a*d*f*x - I*a*c*f + (a*d*f*x + a*c*f)*e^(f*x + e)
), x) + 2*I*(d*x + c)^m)/(a*f*e^(f*x + e) - I*a*f)

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

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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