Optimal. Leaf size=19 \[ \text {Int}\left (\sqrt {c+d x^2} \tanh ^{-1}(a x),x\right ) \]
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Rubi [A]
time = 0.01, 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 \sqrt {c+d x^2} \tanh ^{-1}(a x) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \sqrt {c+d x^2} \tanh ^{-1}(a x) \, dx &=\int \sqrt {c+d x^2} \tanh ^{-1}(a x) \, dx\\ \end {align*}
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Mathematica [A]
time = 4.27, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {c+d x^2} \tanh ^{-1}(a x) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 5.49, size = 0, normalized size = 0.00 \[\int \sqrt {d \,x^{2}+c}\, \arctanh \left (a x \right )\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {c + d x^{2}} \operatorname {atanh}{\left (a x \right )}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \mathrm {atanh}\left (a\,x\right )\,\sqrt {d\,x^2+c} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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