Optimal. Leaf size=23 \[ \text {Int}\left (\frac {(c+d x)^m}{a \cosh (e+f x)+a},x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int \frac {(c+d x)^m}{a+a \cosh (e+f x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(c+d x)^m}{a+a \cosh (e+f x)} \, dx &=\int \frac {(c+d x)^m}{a+a \cosh (e+f x)} \, dx\\ \end {align*}
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Mathematica [A] time = 5.25, size = 0, normalized size = 0.00 \[ \int \frac {(c+d x)^m}{a+a \cosh (e+f x)} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.65, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (d x + c\right )}^{m}}{a \cosh \left (f x + e\right ) + a}, x\right ) \]
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 \[ \int \frac {{\left (d x + c\right )}^{m}}{a \cosh \left (f x + e\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 0, normalized size = 0.00 \[ \int \frac {\left (d x +c \right )^{m}}{a +a \cosh \left (f x +e \right )}\, dx \]
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 \[ \int \frac {{\left (d x + c\right )}^{m}}{a \cosh \left (f x + e\right ) + a}\,{d x} \]
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 \[ \int \frac {{\left (c+d\,x\right )}^m}{a+a\,\mathrm {cosh}\left (e+f\,x\right )} \,d x \]
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 \[ \frac {\int \frac {\left (c + d x\right )^{m}}{\cosh {\left (e + f x \right )} + 1}\, dx}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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