Optimal. Leaf size=12 \[ -\frac {\log (\cos (a+b x))}{b} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {3475} \[ -\frac {\log (\cos (a+b x))}{b} \]
Antiderivative was successfully verified.
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Rule 3475
Rubi steps
\begin {align*} \int \tan (a+b x) \, dx &=-\frac {\log (\cos (a+b x))}{b}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \[ -\frac {\log (\cos (a+b x))}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 14, normalized size = 1.17 \[ -\frac {\log \left (-\cos \left (b x + a\right )\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 18, normalized size = 1.50 \[ -\frac {\log \left (\frac {{\left | \cos \left (b x + a\right ) \right |}}{{\left | b \right |}}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 1.00 \[ \frac {\ln \left (\sec \left (b x +a \right )\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 18, normalized size = 1.50 \[ -\frac {\log \left (-\sin \left (b x + a\right )^{2} + 1\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.51, size = 16, normalized size = 1.33 \[ \frac {\ln \left ({\mathrm {tan}\left (a+b\,x\right )}^2+1\right )}{2\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sin {\left (a + b x \right )} \sec {\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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