3.151 \(\int (c+d x)^m (a+i a \sinh (e+f x))^n \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.0514336, 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 = {} \[ \int (c+d x)^m (a+i a \sinh (e+f x))^n \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 3.91554, size = 0, normalized size = 0. \[ \int (c+d x)^m (a+i a \sinh (e+f x))^n \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.048, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( a+ia\sinh \left ( fx+e \right ) \right ) ^{n}\, 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))^n,x)

[Out]

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

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

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (d x + c\right )}^{m} \left (\frac{1}{2} \,{\left (i \, a e^{\left (2 \, f x + 2 \, e\right )} + 2 \, a e^{\left (f x + e\right )} - i \, a\right )} e^{\left (-f x - e\right )}\right )^{n}, x\right ) \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))^n,x, algorithm="fricas")

[Out]

integral((d*x + c)^m*(1/2*(I*a*e^(2*f*x + 2*e) + 2*a*e^(f*x + e) - I*a)*e^(-f*x - e))^n, x)

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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))**n,x)

[Out]

Timed out

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

[Out]

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