∫ sec(x) tan (x) dx
To find the integral of sec(x) tan(x) with respect to x, we can use a substitution technique
To find the integral of sec(x) tan(x) with respect to x, we can use a substitution technique.
Let’s start by using the substitution u = sec(x). Therefore, du/dx = sec(x) tan(x).
Now, we need to rewrite the integral using u.
∫ sec(x) tan(x) dx = ∫ du
Since the derivative of u with respect to x is du/dx, we rearrange and substitute back.
∫ du = ∫ du/dx dx
We can see that du/dx = sec(x) tan(x), so we substitute it back into the integral:
∫ du/dx dx = ∫ du
Now, we can integrate du with respect to u:
∫ du = u + C
Since u = sec(x), we can substitute it back into the result:
∫ sec(x) tan(x) dx = sec(x) + C
Therefore, the integral of sec(x) tan(x) with respect to x is sec(x) + C, where C is the constant of integration.
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