Final answer to the problem
$\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)+C_0$
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1
The integral of the secant function is given by the following formula, $\displaystyle\int\sec(x)dx=\ln\left|\sec(x)+\tan(x)\right|$
$\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)$
2
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
$\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)+C_0$
Final answer to the problem
$\ln\left(\sec\left(x\right)+\tan\left(x\right)\right)+C_0$