SOLUTION: integrate sec^2x dx

Question 1141352: integrate sec^2x dx
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
integral of sec^2 (x) dx = integral of 1/cos^2 (x) dx =
:
((sin^2 (x) + cos^2 (x))/cos^2 (x)) dx
:
I used the identity sin^2 (x) + cos^2 (x) = 1
:
Note the derivative of sin(x)/cos(x) = ((cos(x) * cos(x) - sin(x) * -sin(x))/cos^2 (x)) dx = ((cos^2 (x)+ sin^2 (x))/cos^2 (x)) dx = (1/cos^2 (x)) dx = sec^2 (x) dx
:
let u = tan(x) = sin(x)/cos(x)
:
du = (1/cos^2 (x)) dx, then
:
******************************************************************
integral of sec^2 (x) dx = integral of u du = u = tan(x) +constant
******************************************************************
:
RELATED QUESTIONS
integral calculus 1. integrate the dx/e^x-e^-x 2. integrate the sec^2xdx/8+sec^2x 3. (answered by Alan3354)

integrate... (answered by Alan3354)

integrate 2x^3/(sqrt[1-x^4])... (answered by Alan3354)

integrate 2x^3 / [sqr(1-x^4)]... (answered by dfrazzetto)

Can u please help me integrate { xsec^2x... (answered by rothauserc)

integrate sin^2 x... (answered by Alan3354)

Integrate... (answered by ikleyn)

integrate {{{ 6x^5 * e^x^6 }}}... (answered by ikleyn)

Pls help me solve this, Integrate sec^2 x/(2+tanx)(3-tanx) dx (Hint: t=tanx) Thank... (answered by Edwin McCravy)