Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^4}{a+b \text {sech}\left (c+d x^2\right )},x\right ) \]
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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 = {} \[ \int \frac {x^4}{a+b \text {sech}\left (c+d x^2\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x^4}{a+b \text {sech}\left (c+d x^2\right )} \, dx &=\int \frac {x^4}{a+b \text {sech}\left (c+d x^2\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 8.73, size = 0, normalized size = 0.00 \[ \int \frac {x^4}{a+b \text {sech}\left (c+d x^2\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{4}}{b \operatorname {sech}\left (d x^{2} + c\right ) + a}, x\right ) \]
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 \[ \int \frac {x^{4}}{b \operatorname {sech}\left (d x^{2} + c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.32, size = 0, normalized size = 0.00 \[ \int \frac {x^{4}}{a +b \,\mathrm {sech}\left (d \,x^{2}+c \right )}\, dx \]
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 \[ \frac {x^{5}}{5 \, a} - 2 \, b \int \frac {x^{4} e^{\left (d x^{2} + c\right )}}{a^{2} e^{\left (2 \, d x^{2} + 2 \, c\right )} + 2 \, a b e^{\left (d x^{2} + c\right )} + a^{2}}\,{d x} \]
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 \[ \int \frac {x^4}{a+\frac {b}{\mathrm {cosh}\left (d\,x^2+c\right )}} \,d x \]
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 \[ \int \frac {x^{4}}{a + b \operatorname {sech}{\left (c + d x^{2} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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