Integrating ∫sec²(x)dx using the tan(x) derivative formula: A Step-by-Step Guide

∫sec²(x)dx =

To integrate ∫sec²(x)dx, we can use the integral formula for the derivative of the tan(x) function:

∫sec²(x)dx = tan(x) + C

Where C is the constant of integration

To integrate ∫sec²(x)dx, we can use the integral formula for the derivative of the tan(x) function:

∫sec²(x)dx = tan(x) + C

Where C is the constant of integration.

To verify this, we’ll differentiate tan(x) to confirm that its derivative is indeed sec²(x).

Using the quotient rule, we have:

dy/dx = (sin(x)cos(x) – cos(x)sin(x))/(cos²(x))

= (sin(x)cos(x) – sin(x)cos(x))/(cos²(x))

= 0/cos²(x)

= 0

Therefore, the derivative of tan(x) is indeed sec²(x).

Thus, ∫sec²(x)dx = tan(x) + C

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