Optimal. Leaf size=21 \[ \text {Int}\left (x^4 \left (a+b \text {csch}\left (c+d x^2\right )\right )^2,x\right ) \]
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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 = {} \[ \int x^4 \left (a+b \text {csch}\left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^4 \left (a+b \text {csch}\left (c+d x^2\right )\right )^2 \, dx &=\int x^4 \left (a+b \text {csch}\left (c+d x^2\right )\right )^2 \, dx\\ \end {align*}
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Mathematica [A] time = 34.71, size = 0, normalized size = 0.00 \[ \int x^4 \left (a+b \text {csch}\left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (b^{2} x^{4} \operatorname {csch}\left (d x^{2} + c\right )^{2} + 2 \, a b x^{4} \operatorname {csch}\left (d x^{2} + c\right ) + a^{2} x^{4}, x\right ) \]
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 \[ \int {\left (b \operatorname {csch}\left (d x^{2} + c\right ) + a\right )}^{2} x^{4}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.43, size = 0, normalized size = 0.00 \[ \int x^{4} \left (a +b \,\mathrm {csch}\left (d \,x^{2}+c \right )\right )^{2}\, dx \]
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 \[ \frac {1}{5} \, a^{2} x^{5} - \frac {b^{2} x^{3}}{d e^{\left (2 \, d x^{2} + 2 \, c\right )} - d} + \int \frac {4 \, a b d x^{4} - 3 \, b^{2} x^{2}}{2 \, {\left (d e^{\left (d x^{2} + c\right )} + d\right )}}\,{d x} + \int \frac {4 \, a b d x^{4} + 3 \, b^{2} x^{2}}{2 \, {\left (d e^{\left (d x^{2} + c\right )} - d\right )}}\,{d x} \]
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 \[ \int x^4\,{\left (a+\frac {b}{\mathrm {sinh}\left (d\,x^2+c\right )}\right )}^2 \,d x \]
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 \[ \int x^{4} \left (a + b \operatorname {csch}{\left (c + d x^{2} \right )}\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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