Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2},x\right ) \]
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Rubi [A] time = 0.0579459, 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 = {} \[ \int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx &=\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx\\ \end{align*}
Mathematica [A] time = 55.645, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.47, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) ^{2} \left ( a+b\sinh \left ( fx+e \right ) \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{2 \,{\left (a e^{\left (f x + e\right )} - b\right )}}{a^{2} b c^{2} f + b^{3} c^{2} f +{\left (a^{2} b d^{2} f + b^{3} d^{2} f\right )} x^{2} + 2 \,{\left (a^{2} b c d f + b^{3} c d f\right )} x -{\left (a^{2} b c^{2} f e^{\left (2 \, e\right )} + b^{3} c^{2} f e^{\left (2 \, e\right )} +{\left (a^{2} b d^{2} f e^{\left (2 \, e\right )} + b^{3} d^{2} f e^{\left (2 \, e\right )}\right )} x^{2} + 2 \,{\left (a^{2} b c d f e^{\left (2 \, e\right )} + b^{3} c d f e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )} - 2 \,{\left (a^{3} c^{2} f e^{e} + a b^{2} c^{2} f e^{e} +{\left (a^{3} d^{2} f e^{e} + a b^{2} d^{2} f e^{e}\right )} x^{2} + 2 \,{\left (a^{3} c d f e^{e} + a b^{2} c d f e^{e}\right )} x\right )} e^{\left (f x\right )}} + \int \frac{2 \,{\left (2 \, b d -{\left (a d f x e^{e} +{\left (c f e^{e} + 2 \, d e^{e}\right )} a\right )} e^{\left (f x\right )}\right )}}{a^{2} b c^{3} f + b^{3} c^{3} f +{\left (a^{2} b d^{3} f + b^{3} d^{3} f\right )} x^{3} + 3 \,{\left (a^{2} b c d^{2} f + b^{3} c d^{2} f\right )} x^{2} + 3 \,{\left (a^{2} b c^{2} d f + b^{3} c^{2} d f\right )} x -{\left (a^{2} b c^{3} f e^{\left (2 \, e\right )} + b^{3} c^{3} f e^{\left (2 \, e\right )} +{\left (a^{2} b d^{3} f e^{\left (2 \, e\right )} + b^{3} d^{3} f e^{\left (2 \, e\right )}\right )} x^{3} + 3 \,{\left (a^{2} b c d^{2} f e^{\left (2 \, e\right )} + b^{3} c d^{2} f e^{\left (2 \, e\right )}\right )} x^{2} + 3 \,{\left (a^{2} b c^{2} d f e^{\left (2 \, e\right )} + b^{3} c^{2} d f e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )} - 2 \,{\left (a^{3} c^{3} f e^{e} + a b^{2} c^{3} f e^{e} +{\left (a^{3} d^{3} f e^{e} + a b^{2} d^{3} f e^{e}\right )} x^{3} + 3 \,{\left (a^{3} c d^{2} f e^{e} + a b^{2} c d^{2} f e^{e}\right )} x^{2} + 3 \,{\left (a^{3} c^{2} d f e^{e} + a b^{2} c^{2} d f e^{e}\right )} x\right )} e^{\left (f x\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} +{\left (b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right )} \sinh \left (f x + e\right )^{2} + 2 \,{\left (a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right )} \sinh \left (f x + e\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (d x + c\right )}^{2}{\left (b \sinh \left (f x + e\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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