Integrand size = 9, antiderivative size = 9 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\sec (x)}}{\log (2)} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {4424, 2240} \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\sec (x)}}{\log (2)} \]
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Rule 2240
Rule 4424
Rubi steps \begin{align*} \text {integral}& = -\text {Subst}\left (\int \frac {2^{\frac {1}{x}}}{x^2} \, dx,x,\cos (x)\right ) \\ & = \frac {2^{\sec (x)}}{\log (2)} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\sec (x)}}{\log (2)} \]
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Time = 21.10 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.11
method | result | size |
derivativedivides | \(\frac {2^{\sec \left (x \right )}}{\ln \left (2\right )}\) | \(10\) |
default | \(\frac {2^{\sec \left (x \right )}}{\ln \left (2\right )}\) | \(10\) |
risch | \(\frac {2^{\sec \left (x \right )}}{\ln \left (2\right )}\) | \(10\) |
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none
Time = 0.24 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\left (\frac {1}{\cos \left (x\right )}\right )}}{\log \left (2\right )} \]
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Time = 0.17 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\sec {\left (x \right )}}}{\log {\left (2 \right )}} \]
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none
Time = 0.20 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\sec \left (x\right )}}{\log \left (2\right )} \]
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none
Time = 0.29 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\left (\frac {1}{\cos \left (x\right )}\right )}}{\log \left (2\right )} \]
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Time = 27.58 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.22 \[ \int 2^{\sec (x)} \sec (x) \tan (x) \, dx=\frac {2^{\frac {1}{\cos \left (x\right )}}}{\ln \left (2\right )} \]
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