Optimal. Leaf size=10 \[ \frac {\sec (a+b x)}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2606, 8} \[ \frac {\sec (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 8
Rule 2606
Rubi steps
\begin {align*} \int \sec (a+b x) \tan (a+b x) \, dx &=\frac {\operatorname {Subst}(\int 1 \, dx,x,\sec (a+b x))}{b}\\ &=\frac {\sec (a+b x)}{b}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.00 \[ \frac {\sec (a+b x)}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 12, normalized size = 1.20 \[ \frac {1}{b \cos \left (b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 12, normalized size = 1.20 \[ \frac {1}{b \cos \left (b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 11, normalized size = 1.10 \[ \frac {\sec \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 12, normalized size = 1.20 \[ \frac {1}{b \cos \left (b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.52, size = 20, normalized size = 2.00 \[ -\frac {2}{b\,\left ({\mathrm {tan}\left (\frac {a}{2}+\frac {b\,x}{2}\right )}^2-1\right )} \]
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 \[ \int \sin {\left (a + b x \right )} \sec ^{2}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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