Optimal. Leaf size=25 \[ \text {Int}\left (\frac {x^m \cosh (c+d x)}{a+b \sinh (c+d x)},x\right ) \]
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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 = {} \[ \int \frac {x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx &=\int \frac {x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx\\ \end {align*}
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Mathematica [A] time = 5.25, size = 0, normalized size = 0.00 \[ \int \frac {x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{m} \cosh \left (d x + c\right )}{b \sinh \left (d x + c\right ) + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \cosh \left (d x + c\right )}{b \sinh \left (d x + c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \cosh \left (d x +c \right )}{a +b \sinh \left (d x +c \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {x e^{\left (2 \, d x + m \log \relax (x) + 2 \, c\right )}}{b {\left (m + 1\right )} e^{\left (2 \, d x + 2 \, c\right )} + 2 \, a {\left (m + 1\right )} e^{\left (d x + c\right )} - b {\left (m + 1\right )}} - \frac {1}{2} \, \int \frac {2 \, {\left (2 \, a d x e^{\left (3 \, d x + 3 \, c\right )} - 2 \, a {\left (m + 1\right )} e^{\left (d x + c\right )} + b {\left (m + 1\right )} - {\left (2 \, b d x e^{\left (2 \, c\right )} + b {\left (m + 1\right )} e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )}\right )} x^{m}}{b^{2} {\left (m + 1\right )} e^{\left (4 \, d x + 4 \, c\right )} + 4 \, a b {\left (m + 1\right )} e^{\left (3 \, d x + 3 \, c\right )} - 4 \, a b {\left (m + 1\right )} e^{\left (d x + c\right )} + b^{2} {\left (m + 1\right )} + 2 \, {\left (2 \, a^{2} {\left (m + 1\right )} e^{\left (2 \, c\right )} - b^{2} {\left (m + 1\right )} e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^m\,\mathrm {cosh}\left (c+d\,x\right )}{a+b\,\mathrm {sinh}\left (c+d\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \cosh {\left (c + d x \right )}}{a + b \sinh {\left (c + d x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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