If u = 1 + tan^2(theta), du = 2tan(theta)*sec^2(theta)d(theta)Punkyc7 said:Homework Statement
integral of cos^2 * (sqr(1+tan^2))
Homework Equations
The Attempt at a Solution
let u = 1 +tan^2
du = sec^2
Punkyc7 said:im not sure how 1/cos^2 gets accounted for the cos^2 in the front
The process for solving this integral involves using a trigonometric identity to rewrite cos^2*sqrt(u) as a function of u, and then applying the power rule for integrals to solve for the antiderivative.
You can use the identity cos^2(x) = (1 + cos(2x))/2 to rewrite cos^2*sqrt(u) as (1 + cos(2*sqrt(u)))/2. Then, substitute u for x to get the final form of the integral.
Yes, this integral can be solved using substitution. You can substitute u = x^2 and then use the chain rule to rewrite the integral in terms of u. However, using a trigonometric identity may be a simpler and more direct approach.
No, there is no specific range of values for u that this integral can be solved for. It can be solved for any value of u, as long as you use the appropriate trigonometric identity and apply the power rule for integrals correctly.
One helpful tip for solving this integral is to use the half-angle formula for cosine, which states that cos^2(x) = (1 + cos(2x))/2. This can make the integration process simpler and more straightforward.