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

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.06, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 32.31, size = 0, normalized size = 0.00 \[ \int \frac {x^m \sinh ^3(c+d x)}{a+b \cosh (c+d x)} \, dx \]

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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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a}\,{d x} \]

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)

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maple [A]  time = 0.21, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \left (\sinh ^{3}\left (d x +c \right )\right )}{a +b \cosh \left (d x +c \right )}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \sinh \left (d x + c\right )^{3}}{b \cosh \left (d x + c\right ) + a}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^m\,{\mathrm {sinh}\left (c+d\,x\right )}^3}{a+b\,\mathrm {cosh}\left (c+d\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \sinh ^{3}{\left (c + d x \right )}}{a + b \cosh {\left (c + d x \right )}}\, dx \]

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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