Find the most general antiderivative of the function use the

Solution

let\'s write it out in sine\'s and cosines h(x) = 4(1/cos x)*(sin x/cos x) = 4 sin x /cos^2 x now lets substitute u = cos x du = - sin x we then have h(x) = -4 (1/u^2)du integral is 4(1/u) + C change back to starting variable 4 sec x + c let\'s check our work using the quotient rule (denominator times deriv of numerator) minus (numerator time derviv of denom) all over denom squared (d/dx)1/cos x = [(cos x)(0) - (1)(-sinx)]/cos^2x = [sin x]/cos^2 x = sec x * tan x yes, it works!