Optimal. Leaf size=22 \[ b \text {Int}\left (\frac {\sec \left (c+d x^2\right )}{x},x\right )+a \log (x) \]
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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 = {} \[ \int \frac {a+b \sec \left (c+d x^2\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {a+b \sec \left (c+d x^2\right )}{x} \, dx &=\int \left (\frac {a}{x}+\frac {b \sec \left (c+d x^2\right )}{x}\right ) \, dx\\ &=a \log (x)+b \int \frac {\sec \left (c+d x^2\right )}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.77, size = 0, normalized size = 0.00 \[ \int \frac {a+b \sec \left (c+d x^2\right )}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.70, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b \sec \left (d x^{2} + c\right ) + a}{x}, x\right ) \]
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 \[ \int \frac {b \sec \left (d x^{2} + c\right ) + a}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.76, size = 0, normalized size = 0.00 \[ \int \frac {a +b \sec \left (d \,x^{2}+c \right )}{x}\, dx \]
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 \[ 2 \, b \int \frac {\cos \left (2 \, d x^{2} + 2 \, c\right ) \cos \left (d x^{2} + c\right ) + \sin \left (2 \, d x^{2} + 2 \, c\right ) \sin \left (d x^{2} + c\right ) + \cos \left (d x^{2} + c\right )}{x \cos \left (2 \, d x^{2} + 2 \, c\right )^{2} + x \sin \left (2 \, d x^{2} + 2 \, c\right )^{2} + 2 \, x \cos \left (2 \, d x^{2} + 2 \, c\right ) + x}\,{d x} + a \log \relax (x) \]
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 \[ \int \frac {a+\frac {b}{\cos \left (d\,x^2+c\right )}}{x} \,d x \]
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 \[ \int \frac {a + b \sec {\left (c + d x^{2} \right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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