How do you find the integral of int 2secxtanx dx?

1 Answer
Sep 26, 2015

2secx+C

Explanation:

I=int 2secxtanxdx=2int (secx)'dx=2intd(secx)

I=2secx+C

Explanation:

(secx)' = secxtanx => 2secxtanx = 2(secx)'

I = int 2secxtanxdx = 2 int (secx)'dx

Differential of a function is defined as:

d(f(x)) = f'(x)dx => d(secx) = (secx)'dx

I = 2 int (secx)'dx = 2 int d(secx)

Elementary formula from integration theory:

int d(f(x)) = f(x) + C

I = 2 int d(secx) = 2secx + C