This section: 4. Integrals of trigonometric functions

derivative rule antiderivative rule
d dx sin x = cos x cos x dx = sin x + C
d dx cos x = − sin x sin x dx = − cos x + C
d dx tan x = sec2x sec2x dx = tan x + C
d dx cotan x = − cosec2x cosec2x dx = − cotan x + C

With that in mind, what are the integrals of trigonometric functions?

Integral of trigonometric functions

Function Integral
tanx = sec2x -ln|cosx| + c
cotx = -csc2x ln|sinx| + c
secx ln|secx + tanx| + c
cscx -ln|cscx + cotx| + c

Also, what is the integral of COTX?

Integral cot(x) cot x = ln |sin x| + C.

Then how do you integrate cos 2x?

The integral of cos(2x) is (1/2)sin(2x) + C, where C is a constant.

What is the antiderivative of cos?

Direct link to Noble Mushtak’s post “The derivative of cos(x) is –sin(x). The derivative of cos(x) is –sin(x), but the antiderivative of cos(x) is sin(x)+C.

How to calculate arctan?

Press the “Shift” key of the calculator.” “2.” or “function” key and then press the “tan” key. Enter the number whose arctan you want to find. For this example, enter the number “0.577”. Press the “=” key.

What is the inverse tangent integral?

The inverse tangent integral. We can use dv = set dx and therefore say that v = ∫ dx = x.

How to integrate CSC?

Integral csc(x) csc x = – ln|csc x + cot x| + C.

How do you integrate?

An “S” shaped symbol is used to denote the integral of and dx is placed at the end of the terms to be integrated, which means ” with respect to x” means the s is call “dx” which appears in dy/dx. To integrate an expression, raise its power by 1 and divide by that number.

What is the integral of negative cosine? Math Tables: Table of Integrals

sin x dx = –cos x + C proof csc x dx = – ln|csc x + cot x| + C-proof
cos x dx = sin x + C-proof sec x dx = ln|sec x + tan x| + C proof
tan x dx = -ln|cos x| + C proof cot x dx = ln |sin x| + C Proof

What is an arcsine?

Arcsine definition. The arcsine of x is the inverse Sine function of x defined when -1≤x≤1. If the sine of y is equal to x: sin y = x. Then the arcsine of x is equal to the inverse sine function of x, which is equal to y: arcsin x = sin -1 x = y.

What is secX?

The secondary trigonometric functions are cosecans, secans, and cotangents [csc, sec, cot]. They are ratios relating side lengths (opposite, adjacent, hypotenuse) to an angle in a right triangle. So secX is simply the ratio of the length of a hypotenuse to the length of an adjacent side.