We learned about the **Inverse Trig Functions** here, and it turns out that the derivatives of them are not trig expressions, but **algebraic**. When memorizing these, remember that the functions starting with “**c**” are negative, and the functions with **tan** and **cot** don’t have a square root.

Also remember that sometimes you see the inverse trig function written as \(\arcsin x\) and sometimes you see \({{\sin }^{{-1}}}x\).

# Derivatives of Inverse Trig Functions

Here are the derivatives of Inverse Trigonometric Functions:

Let’s try some problems:

# Integrals of the Inverse Trig Functions

When we integrate Inverse Trigonometric Functions, we have use tricks to get the functions one of the inverse trig forms and then usually use **U-Substitution Integration** to perform the integral.

Here are the integration formulas for the Inverse Trig Functions; notice that we only have formulas for **three of the inverse trig functions**; trust me, it works this way!

To the right of each formula, I’ve included a short-cut formula that you may want to learn; however, if you just know the first formulas at the left (that resemble the differentiation formulas), you will be able to use U-substitution to solve the problems.

A lot of times, to get the integral in the correct form, we have to play with the function to get a “1” in the denominator, either in the square root, or without it (for tan and cot). To do this, just take the greatest common factor (GCF) of the constant out, so a “1” will remain; we’ll see this in problems below.

Let’s first do some **Inverse Trig** **Indefinite Integration** problems: