3.233 \(\int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx\)

Optimal. Leaf size=26 \[ \text{Unintegrable}\left (\frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)},x\right ) \]

[Out]

Unintegrable[(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]), x]

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Rubi [A]  time = 0.0637631, 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 = {} \[ \int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]

[Out]

Defer[Int][(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]), x]

Rubi steps

\begin{align*} \int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx &=\int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx\\ \end{align*}

Mathematica [A]  time = 31.0466, size = 0, normalized size = 0. \[ \int \frac{x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]),x]

[Out]

Integrate[(x^m*Sinh[c + d*x]^3)/(a + b*Cosh[c + d*x]), x]

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Maple [A]  time = 0.054, size = 0, normalized size = 0. \begin{align*} \int{\frac{{x}^{m} \left ( \sinh \left ( dx+c \right ) \right ) ^{3}}{a+b\cosh \left ( dx+c \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*sinh(d*x+c)^3/(a+b*cosh(d*x+c)),x)

[Out]

int(x^m*sinh(d*x+c)^3/(a+b*cosh(d*x+c)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sinh(d*x+c)^3/(a+b*cosh(d*x+c)),x, algorithm="maxima")

[Out]

integrate(x^m*sinh(d*x + c)^3/(b*cosh(d*x + c) + a), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sinh(d*x+c)^3/(a+b*cosh(d*x+c)),x, algorithm="fricas")

[Out]

integral(x^m*sinh(d*x + c)^3/(b*cosh(d*x + c) + a), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x^{m} \sinh ^{3}{\left (c + d x \right )}}{a + b \cosh{\left (c + d x \right )}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*sinh(d*x+c)**3/(a+b*cosh(d*x+c)),x)

[Out]

Integral(x**m*sinh(c + d*x)**3/(a + b*cosh(c + d*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sinh(d*x+c)^3/(a+b*cosh(d*x+c)),x, algorithm="giac")

[Out]

integrate(x^m*sinh(d*x + c)^3/(b*cosh(d*x + c) + a), x)