∫secxtanxdx
To find the integral of sec(x)tan(x) dx, we can use a substitution method
To find the integral of sec(x)tan(x) dx, we can use a substitution method. Let’s try substituting u = sec(x).
First, find the derivative of u with respect to x:
du/dx = sec(x)tan(x) dx
We have sec(x)tan(x) dx in the original integral and we have du/dx in terms of sec(x)tan(x) dx. Thus, we can rewrite the integral as:
∫sec(x)tan(x) dx = ∫du/dx dx
Now, we can rewrite the integral using substitution:
∫du/dx dx = ∫du
Since du/dx = sec(x)tan(x) dx, we can simplify the integral to:
∫sec(x)tan(x) dx = ∫du
Integrating du is straightforward:
∫du = u + C
Recall that u = sec(x), so substitute that back in:
∫sec(x)tan(x) dx = sec(x) + C
Thus, the integral of sec(x)tan(x) dx is sec(x) + C, where C is the constant of integration.
More Answers:
[next_post_link]