Optimal. Leaf size=21 \[ \text {Int}\left (x^2 \left (a+b \text {sech}\left (c+d x^2\right )\right )^2,x\right ) \]
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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 = {}
\begin {gather*} \int x^2 \left (a+b \text {sech}\left (c+d x^2\right )\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int x^2 \left (a+b \text {sech}\left (c+d x^2\right )\right )^2 \, dx &=\int x^2 \left (a+b \text {sech}\left (c+d x^2\right )\right )^2 \, dx\\ \end {align*}
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Mathematica [A]
time = 4.96, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 \left (a+b \text {sech}\left (c+d x^2\right )\right )^2 \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 1.20, size = 0, normalized size = 0.00 \[\int x^{2} \left (a +b \,\mathrm {sech}\left (d \,x^{2}+c \right )\right )^{2}\, dx\]
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 \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 x^{2} \left (a + b \operatorname {sech}{\left (c + d x^{2} \right )}\right )^{2}\, 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 x^2\,{\left (a+\frac {b}{\mathrm {cosh}\left (d\,x^2+c\right )}\right )}^2 \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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