Question

Integrate with respect to x :
∫secxtanxdx

Answer 1

Answer on Question #50933 – Math – Integral Calculus

Integrate with respect to $x$ :

$\int_{\sec x} dx$

Solution

$$\begin{array}{l} \int \sec x \cdot \tan x \, dx = \int \frac{\sin x}{\cos^2 x} \, dx = \\ = \left| u = \sec x, \, du = \left(\frac{1}{\cos x}\right)' \, dx = - \frac{-\sin x}{\cos^2 x} \, dx = \sec x \cdot \tan x \, dx \right| = \\ = \int du = u = \sec x + C, \text{ where } C \text{ is an arbitrary real constant}. \end{array}$$

Answer: $\int_{\sec x} dx = \sec x + C$

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