∫ sec²(x) dx
To find the integral of sec^2(x) dx, we use a method called integration by substitution
To find the integral of sec^2(x) dx, we use a method called integration by substitution.
First, we need to choose our substitution. Let’s choose u = tan(x).
To find du/dx, we differentiate both sides of the equation u = tan(x) with respect to x:
du/dx = sec^2(x)
This is exactly what we need to replace sec^2(x) in our original integral. Rearranging the equation, we have:
du = sec^2(x) dx
Now we can replace sec^2(x) dx in the original integral with du:
∫ sec^2(x) dx = ∫ du
Integrating du is straightforward:
∫ du = u + C
Substituting u back in terms of x, we have:
∫ sec^2(x) dx = tan(x) + C
Therefore, the integral of sec^2(x) dx is tan(x) + C, where C is the constant of integration.
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