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 = sec^{2}x |
sec^{2}x dx = tan x + C |

d dx cotan x = − cosec^{2}x |
cosec^{2}x dx = − cotan x + C |

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

**Integral** of **trigonometric** functions

Function | Integral |
---|---|

tanx = sec^{2}x |
-ln|cosx| + c |

cotx = -csc^{2}x |
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?

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 |

## 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.