**The formula for the integral of ln x is given by, ∫ln x dx = xlnx – x + C, where C is the constant of integration.**

Likewise, What is the derivative of Secx?

The derivative of sec x is **sec x tan x** whereas the derivative of sec^{–}^{1}x is 1/(x √x² – 1).

As well, How do you find the antiderivative of LNX? The antiderivative of ln x is **equal to the difference of x ln x and x plus the constant of integration**. Mathematically, we can write the antiderivative of ln x as ∫ ln x dx = x ln x – x + C, where C is the integration constant.

How do you do Lnx Antiderive?

Moreover What is the antiderivative of Arctan? The integral of arctan is the integration of **tan inverse x**, which is also called the antiderivative of arctan, which is given by ∫tan^{–}^{1}x dx = x tan^{–}^{1}x – ½ ln |1+x^{2}| + C, where C is the constant of integration.

**What is Arcsin derivative?**

What is Derivative of arcsin? The derivative of arcsin x is **1/√1-x²**. It is written as d/dx(arcsin x) = 1/√1-x².

**What is FX Secx Cscx FX?**

**What is the antiderivative of SEC 2x?**

and the general antiderivative of sec2x is **tanx+C** .

**What is antiderivative sin?**

The general antiderivative of sin(x) is **−cos(x)+C** .

**What is the antiderivative of Sec 2?**

and the general antiderivative of sec2x is **tanx+C** .

**What are the antiderivative rules?**

** The antiderivative rules of the six trigonometric functions are as follows: **

- ∫sin x dx = -cos x + C.
- ∫cos x dx = sin x + C.
- ∫tan x dx = ln |sec x| + C.
- ∫cot x dx = ln |sin x| + C.
- ∫sec x dx = ln |sec x + tan x| + C.
- ∫csc x dx = ln |cosec x – cot x| + C.

**What is the arctan of infinity?**

Showing that the limit, as x approaches infinity, of arctan(x) is **Pi/2** .

**What is the antiderivative of Arccos?**

Now, that we have derived the derivative of arccos, we will find the anti-derivative of arccos, that is, **∫arccos x dx = ∫cos ^{–}^{1} x dx** using the integration by parts (ILATE).

**Is arctan and tan 1 the same?**

The inverse is used to obtain the measure of an angle using the ratios from basic right triangle trigonometry. **The inverse of tangent is denoted as Arctangent or on a calculator it will appear as atan or tan ^{–}^{1}**.

**What is arcsec equivalent to?**

sec x = 1/(cos x) ⇒ Arcsec x = **Arccos(1/x)** csc x = 1/(sin x) ⇒ Arccsc x = Arcsin(1/x) This means that Arcsec and Arccsc have the same ranges as Arccos and Arcsin, respectively.

**What is Arctan derivative?**

The derivative of arctan x is **1/(1+x ^{2})**. i.e., d/dx(arctan x) = 1/(1+x

^{2}). This also can be written as d/dx(tan

^{–}

^{1}x) = 1/(1+x

^{2}).

**Is arcsin the same as 1 sin?**

**Arcsine is the inverse of sine function**. It is used to evaluate the angle whose sine value is equal to the ratio of its opposite side and hypotenuse.

**What is Cscx?**

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = **1 sin x** .

**What is the derivative of csc?**

cscx=**1sinx**. From Derivative of Sine Function: ddx(sinx)=cosx.

**How do you differentiate Sec 2?**

Answer and Explanation: The derivative of sec2 (x) is **2sec2 (x) tan (x)**. The chain rule states that the derivative of f(g(x)) is equal to f ‘ (g(x)) ⋅ g ‘ (x)….

**What is the integral of Sec 2?**

Math2.org Math Tables: Table of Integrals

cos x dx = sin x + C Proof | csc x cot x dx = – csc x + C Proof |
---|---|

sin x dx = -cos x + C Proof | sec x tan x dx = sec x + C Proof |

sec ^{ 2 } x dx = tan x + C Proof |
csc ^{ 2 } x dx = – cot x + C Proof |

**What is the antiderivative of Cscx?**

Solution. We’ve found that the integral of cscx is **-ln |cscx + cotx| + C**.

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

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

**What is the antiderivative of E X?**

Therefore, every antiderivative of ex is of the form **ex+C** for some constant C and every function of the form ex+C is an antiderivative of ex.

**What is the antiderivative of Cscx?**

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 use Antidifferentiate sin and cos?**

Anti-derivatives of trig functions can be found exactly as the reverse of derivatives of trig functions. **The anti-derivative of sinx is −cosx+C and the anti-derivative of cosx is sinx+C**.