Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )} \, dx &=\int \frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.40, size = 0, normalized size = 0.00 \[ \int \frac {1}{(d+e x)^2 \left (a+b \cosh ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.60, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a e^{2} x^{2} + 2 \, a d e x + a d^{2} + {\left (b e^{2} x^{2} + 2 \, b d e x + b d^{2}\right )} \operatorname {arcosh}\left (c x\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (e x + d\right )}^{2} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.46, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e x +d \right )^{2} \left (a +b \,\mathrm {arccosh}\left (c x \right )\right )}\, dx \]
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 \[ \int \frac {1}{{\left (e x + d\right )}^{2} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )\,{\left (d+e\,x\right )}^2} \,d x \]
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 \[ \int \frac {1}{\left (a + b \operatorname {acosh}{\left (c x \right )}\right ) \left (d + e x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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