What is the Antiderivative of trig functions?

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

Subsequently, one may also ask, what are the integrals of trig functions?

Integrals 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

Furthermore, what is the integral of COTX? Integral cot(x) cot x = ln|sin x| + C.

Hereof, how do you integrate Cos 2x?

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

What is 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). However, the antiderivative of cos(x) is sin(x)+C.

What is the integral of negative cosine?

Math2.org 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

How do you integrate?

A "S" shaped symbol is used to mean the integral of, and dx is written at the end of the terms to be integrated, meaning "with respect to x". This is the same "dx" that appears in dy/dx . To integrate a term, increase its power by 1 and divide by this figure.

What is secX?

The secondary trig functions are cosecant, secant, and cotangent [csc, sec, cot]. They are ratios that relate side lengths (opposite, adjacent, hypotenuse) to an angle in a right triangle. So secX is just the ratio of the length of a hypotenuse to the length of an adjacent side.

What is the integral of inverse tangent?

The Integral of Inverse TangentWe can set dv = dx and, therefore ,say that v = ∫ dx = x.

What is an Arcsin?

Arcsin definitionThe arcsine of x is defined as the inverse sine function of x when -1≤x≤1. When 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.

How do you integrate CSC?

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

How do you do Arctan?

Press the calculator's "shift," "2nd" or "function" key, and then press the "tan" key. Type the number whose arctan you want to find. For this example, type in the number "0.577." Press the "=" button.