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 = 18, normalized size = 1.50 \[ -\frac {\log \left (\frac {1}{\tan \left (b x + a\right )^{2} + 1}\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 13, normalized size = 1.08 \[ -\frac {\log \left ({\left | \cos \left (b x + a\right ) \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 1.42 \[ \frac {\ln \left (\tan ^{2}\left (b x +a \right )+1\right )}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 11, normalized size = 0.92 \[ \frac {\log \left (\sec \left (b x + a\right )\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.23, 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 [A] time = 0.13, size = 19, normalized size = 1.58 \[ \begin {cases} \frac {\log {\left (\tan ^{2}{\left (a + b x \right )} + 1 \right )}}{2 b} & \text {for}\: b \neq 0 \\x \tan {\relax (a )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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