2sec^4x dx Evaluate the integral?

Answer 1

Nasty, nasty. Tell your math teacher that I like them a lot ☺

By parts (2/3)*(sec(x)^2 + 2)*tan(x)

Now go work it yourself. Problems such as this one develop character ☺


Doug

Answer 2

Something is missing here.

Do you mean 2sec^4x x dx? or 2sec^4 x dx?

You have not stated what the angle associated with the secant is.

Answer 3

sec(x)^2 dx = tan(x)

sec(x)^4 dx = [(tan(x)^2 + 1]sec(x)^2 dx = [tan(x)^2 * sec(x)^2 dx + sec(x)^2 dx

Use u = tan(x), du = sec(x)^2 dx, and you get sec^4 x dx = (u^3)/3 + u + c = [tan(x)^3]/3 + tan(x) + c}


(To get Dougs expression, just multiply by 2)

Ana