Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x) (a+b \tan (e+f x))},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {1}{(c+d x) (a+b \tan (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(c+d x) (a+b \tan (e+f x))} \, dx &=\int \frac {1}{(c+d x) (a+b \tan (e+f x))} \, dx\\ \end {align*}
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Mathematica [A] time = 1.97, size = 0, normalized size = 0.00 \[ \int \frac {1}{(c+d x) (a+b \tan (e+f x))} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.64, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a d x + a c + {\left (b d x + b c\right )} \tan \left (f x + e\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (d x + c\right )} {\left (b \tan \left (f x + e\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.72, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d x +c \right ) \left (a +b \tan \left (f x +e \right )\right )}\, dx \]
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 = -0.04 \[ \int \frac {1}{\left (a+b\,\mathrm {tan}\left (e+f\,x\right )\right )\,\left (c+d\,x\right )} \,d x \]
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 \[ \int \frac {1}{\left (a + b \tan {\left (e + f x \right )}\right ) \left (c + d x\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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