Optimal. Leaf size=21 \[ \text {Int}\left (x^2 \left (a+b \sec \left (c+d x^2\right )\right )^2,x\right ) \]
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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 = {} \[ \int x^2 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^2 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx &=\int x^2 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx\\ \end {align*}
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Mathematica [A] time = 7.91, size = 0, normalized size = 0.00 \[ \int x^2 \left (a+b \sec \left (c+d x^2\right )\right )^2 \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.62, size = 0, normalized size = 0.00 \[ {\rm integral}\left (b^{2} x^{2} \sec \left (d x^{2} + c\right )^{2} + 2 \, a b x^{2} \sec \left (d x^{2} + c\right ) + a^{2} x^{2}, x\right ) \]
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 \[ \int {\left (b \sec \left (d x^{2} + c\right ) + a\right )}^{2} x^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.98, size = 0, normalized size = 0.00 \[ \int x^{2} \left (a +b \sec \left (d \,x^{2}+c \right )\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
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 \[ \int x^2\,{\left (a+\frac {b}{\cos \left (d\,x^2+c\right )}\right )}^2 \,d x \]
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 \[ \int x^{2} \left (a + b \sec {\left (c + d x^{2} \right )}\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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