Integral Of Tan Theta Math

U sec theta.

Integral of tan theta math. Solve the integral ln u c substitute back u cos x ln cos x c q e d. Tan x dx ln cos x c ln cos x 1 c ln sec x c. This problem is relatively straight forward but for some reason my answer is off by the power of 1. Ln cos x 1 c.

Anytime you have to integrate an expression in the form a 2 x 2 you should think of trig substitution using tan θ. Sec x tan x dx sec x c. Csc2 x dx cot x c. Tanh x dx ln cosh x c.

If we have a right triangle with hypotenuse of length y and one side of length a such that. Click on proof for a proof discussion of a theorem. Ln u c. Substitute back u cos x.

Cosh x dx sinh x c. Sin x cos x sin x dx cos x c. Int tan theta sec 5 theta d theta the steps i take are step 1. V w v w sin θ 1 2 3 2 4 2 2 6 and v w v w cos θ 6 tan θ 6 2 6 θ tan 1 6 2 6 complex number problem i tan theta proof.

X 2 a 2 y 2. Where x is one side of the right triangle a is the other side and y is the hypotenuse. Ln cos x c. The indefinite integral of tangent of x is and it s neat they re connected in this way is the negative natural log of the absolute value of cosine of x plus c.

Reverse chain rule our mission is to provide a free world class education to anyone anywhere. Tan x dx ln cos x c. Cos x sin x cos x dx sin x c. For each of these we simply use the fundamental of calculus because we know their corresponding derivatives.

Coth x dx ln sinh x c. Csc x cot x dx csc x c. Sech x dx arctan sinh x c.