Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{x \left (a+b \sec \left (c+d x^2\right )\right )},x\right ) \]
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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 = {} \[ \int \frac {1}{x \left (a+b \sec \left (c+d x^2\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x \left (a+b \sec \left (c+d x^2\right )\right )} \, dx &=\int \frac {1}{x \left (a+b \sec \left (c+d x^2\right )\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.97, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a+b \sec \left (c+d x^2\right )\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.61, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b x \sec \left (d x^{2} + c\right ) + a x}, x\right ) \]
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 \[ \int \frac {1}{{\left (b \sec \left (d x^{2} + c\right ) + a\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.70, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a +b \sec \left (d \,x^{2}+c \right )\right )}\, dx \]
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 \[ \int \frac {1}{x\,\left (a+\frac {b}{\cos \left (d\,x^2+c\right )}\right )} \,d x \]
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 \[ \int \frac {1}{x \left (a + b \sec {\left (c + d x^{2} \right )}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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