∫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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