Integral Of Secant X Math

D d x tan.

Integral of secant x math. Integration of secant squared of x is an important integral formula in integral calculus and this integral belongs to the trigonometric formulae. Substitute du sec x tan x sec 2 x dx u sec x tan x. Get the answer to integral of sec x 3 with the cymath math problem solver a free math equation solver and math solving app for calculus and algebra. Get the answer to integral of sec x tan x with the cymath math problem solver a free math equation solver and math solving app for calculus and algebra.

Sec x tan x. Substitute du sec x tan x sec 2 x dx u sec x tan x. Sec x tan x. To prove this formula consider.

Sec x tan x. Du sec x tan x sec 2 x dx. The integral of the secant cubed of x is of the form i sec 3 x d x i first we break sec 3 x into sec x and sec 2 x and now the integral i becomes. Sin x sec 3 cos x dx 2 1 sec cos x tan cos x 2 1 ln sec cos x tan cos x next topic.

U sec x tan x. This is just an integral of a secant cubed for which the answer is given by. We then put back v cos x the final answer is. In calculus the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative all of which can be shown to be equivalent via trigonometric identities sec θ d θ 1 2 ln 1 sin θ 1 sin θ c ln sec θ tan θ c ln tan θ 2 π 4 c.

Sec x dx ln sec x tan x c. S e c 3 v dx 2 1 sec v tan v 2 1 ln sec v tan v. U sec x tan x. Sec x dx sec x.

Sec x u sec x tan x u d ln u dx d sec x ln sec x tan x. Sec 2 x d x tan. Sec x tan x. By taking the derivative of exactly the right function and looking at the results in the right way we got the formula we needed.

Du sec x tan x sec 2 x dx.