Integrating ∫sec^2(x) dx Using Trigonometric Identity and Differentiation

∫ sec^2(x) dx

To integrate ∫sec^2(x) dx, we can use a trigonometric identity and the concept of differentiation

To integrate ∫sec^2(x) dx, we can use a trigonometric identity and the concept of differentiation.

The identity we will use is:
d/dx(tan(x)) = sec^2(x)

Let’s start by using this identity to rewrite the integral:
∫sec^2(x) dx = ∫d/dx(tan(x)) dx

Now, we can apply the concept of integration using the inverse operation of differentiation. We will integrate tan(x) with respect to x to obtain the integral of sec^2(x) dx.

∫d/dx(tan(x)) dx = tan(x) + C

Where C is the constant of integration. Thus, the integral of sec^2(x) dx is tan(x) + C.

Note: It is essential to include the constant of integration because when we differentiate tan(x) + C with respect to x, the derivative will be sec^2(x).

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