Question

Find $\int \sec \left(x\right)\tan \left(x\right)dx$

• A. $\text{sec}\left(x\right)+C$
• B. $\text{tan}\left(x\right)+C$
• C. ${\text{sec}}^2\left(x\right)+c$
• D. $\text{ln}|\text{tan}\left(x\right)|+C$

Answer 1

The correct option is A

$\text{sec}\left(x\right)+C$

We want to find the integral of sec(x).tan(x). By integrating a function, we are trying to find/guess a function whose derivative will give the function we are integrating. In this case, we want to find a function whose derivative is sec(x).tan(x). We know that the derivative of sec(x) is sec(x).tan(x). So the integral of sec(x).tan(x) will be sec(x).