Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2},x\right ) \]
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Rubi [A] time = 0.02, 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 = {} \[ \int \frac {\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx &=\int \frac {\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx\\ \end {align*}
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Mathematica [A] time = 17.80, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b \tanh ^{-1}\left (c x^n\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.14, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b^{2} \operatorname {artanh}\left (c x^{n}\right )^{2} + 2 \, a b \operatorname {artanh}\left (c x^{n}\right ) + a^{2}}{x^{2}}, x\right ) \]
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 \[ \int \frac {{\left (b \operatorname {artanh}\left (c x^{n}\right ) + a\right )}^{2}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {\left (a +b \arctanh \left (c \,x^{n}\right )\right )^{2}}{x^{2}}\, dx \]
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 \[ -\frac {b^{2} \log \left (-c x^{n} + 1\right )^{2}}{4 \, x} - \frac {a^{2}}{x} - \int -\frac {{\left (b^{2} c x^{n} - b^{2}\right )} \log \left (c x^{n} + 1\right )^{2} + 4 \, {\left (a b c x^{n} - a b\right )} \log \left (c x^{n} + 1\right ) + 2 \, {\left (2 \, a b + {\left (b^{2} c n - 2 \, a b c\right )} x^{n} - {\left (b^{2} c x^{n} - b^{2}\right )} \log \left (c x^{n} + 1\right )\right )} \log \left (-c x^{n} + 1\right )}{4 \, {\left (c x^{2} x^{n} - x^{2}\right )}}\,{d x} \]
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 \[ \int \frac {{\left (a+b\,\mathrm {atanh}\left (c\,x^n\right )\right )}^2}{x^2} \,d x \]
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 \[ \int \frac {\left (a + b \operatorname {atanh}{\left (c x^{n} \right )}\right )^{2}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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