Optimal. Leaf size=23 \[ \text {Int}\left (\frac {(a+a \sec (e+f x))^2}{(c+d x)^2},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {(a+a \sec (e+f x))^2}{(c+d x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(a+a \sec (e+f x))^2}{(c+d x)^2} \, dx &=\int \frac {(a+a \sec (e+f x))^2}{(c+d x)^2} \, dx\\ \end {align*}
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Mathematica [A]
time = 27.95, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+a \sec (e+f x))^2}{(c+d x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.42, size = 0, normalized size = 0.00 \[\int \frac {\left (a +a \sec \left (f x +e \right )\right )^{2}}{\left (d x +c \right )^{2}}\, dx\]
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*} a^{2} \left (\int \frac {2 \sec {\left (e + f x \right )}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac {\sec ^{2}{\left (e + f x \right )}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac {1}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx\right ) \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 = -0.04 \begin {gather*} \int \frac {{\left (a+\frac {a}{\cos \left (e+f\,x\right )}\right )}^2}{{\left (c+d\,x\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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