secx tanx dx
To evaluate the integral ∫ sec(x) tan(x) dx, we can use a technique called u-substitution
To evaluate the integral ∫ sec(x) tan(x) dx, we can use a technique called u-substitution.
Let’s start by setting u = sec(x). Taking the derivative of both sides with respect to x, we get du/dx = sec(x) tan(x).
From here, we notice that the derivative of u is present in the integrand. Therefore, we can rewrite the integral in terms of u as follows:
∫ sec(x) tan(x) dx = ∫ du
Integrating the right-hand side gives us u + C, where C is the constant of integration.
Substituting the original expression for u, we get:
∫ sec(x) tan(x) dx = sec(x) + C
Thus, the integral of sec(x) tan(x) dx is equal to sec(x) plus a constant.
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