3.3.27 \(\int \frac {x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx\) [227]

Optimal. Leaf size=27 \[ \text {Int}\left (\frac {x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)},x\right ) \]

[Out]

Unintegrable(x^m*sinh(d*x+c)^2/(a+b*cosh(d*x+c)),x)

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Rubi [A]
time = 0.04, 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 = {} \begin {gather*} \int \frac {x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]

[Out]

Defer[Int][(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]), x]

Rubi steps

\begin {align*} \int \frac {x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx &=\int \frac {x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx\\ \end {align*}

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Mathematica [A]
time = 17.61, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^m \sinh ^2(c+d x)}{a+b \cosh (c+d x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]),x]

[Out]

Integrate[(x^m*Sinh[c + d*x]^2)/(a + b*Cosh[c + d*x]), x]

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Maple [A]
time = 0.91, size = 0, normalized size = 0.00 \[\int \frac {x^{m} \left (\sinh ^{2}\left (d x +c \right )\right )}{a +b \cosh \left (d x +c \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*sinh(d*x+c)^2/(a+b*cosh(d*x+c)),x)

[Out]

int(x^m*sinh(d*x+c)^2/(a+b*cosh(d*x+c)),x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sinh(d*x+c)^2/(a+b*cosh(d*x+c)),x, algorithm="maxima")

[Out]

integrate(x^m*sinh(d*x + c)^2/(b*cosh(d*x + c) + a), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sinh(d*x+c)^2/(a+b*cosh(d*x+c)),x, algorithm="fricas")

[Out]

integral(x^m*sinh(d*x + c)^2/(b*cosh(d*x + c) + a), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{m} \sinh ^{2}{\left (c + d x \right )}}{a + b \cosh {\left (c + d x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*sinh(d*x+c)**2/(a+b*cosh(d*x+c)),x)

[Out]

Integral(x**m*sinh(c + d*x)**2/(a + b*cosh(c + d*x)), x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*sinh(d*x+c)^2/(a+b*cosh(d*x+c)),x, algorithm="giac")

[Out]

integrate(x^m*sinh(d*x + c)^2/(b*cosh(d*x + c) + a), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {x^m\,{\mathrm {sinh}\left (c+d\,x\right )}^2}{a+b\,\mathrm {cosh}\left (c+d\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^m*sinh(c + d*x)^2)/(a + b*cosh(c + d*x)),x)

[Out]

int((x^m*sinh(c + d*x)^2)/(a + b*cosh(c + d*x)), x)

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