 parts okay this is not exactly the same as let's go this rule what is this rule this rule is known as first of all there is a sensation so if you have two functions let's say f of x in g of x u is your f these two in this expression into integral of so this term is du by dx because f of now make this the subject of the formula as u times integral integral and this is the formula so in the next half an hour or so we'll do some basic application of this formula as a simple example in this entire this is actually a very important message that this formula gives the message is when you have given to this rule says that function that we write it down somewhere so in his research he said that functions should be chosen at the list first of all a stands for and t stands for trigonometric functions and e stands for exponential functions so he said that higher the function in that list that function should be chosen as u this is the most difficult to integrate this is the most so let's say exponential which one will you choose as you as you become the exponential function in some books they say so i'll start my example by integrating one of the standard functions which we never have to integrate it but we will discuss according to the times u times which is non x integration of the what is integration of one x minus integration of integration of what integration of so what is the u by d we'll put it towards minus integration of one which is x plus c going forward going forward is x times log x minus one this is what should be mellowed for you please include this in the formula just wherever you have seen so far we know the desensiton of sin inverse between the right you know not okay we like to integrate the function actually actually x sin inverse x plus under root one minus x square plus c is the answer for sin inverse okay now there is ways to do it i'll show you both so this is of course u this is of course v so according to the integration where part formula is u times integral of one which is x into x x square as t square so minus x dx will be so this will give you x sin inverse x plus t and t is under root one minus x square so this is the answer for integral of sin inverse x remember the result is possible if possible x sin inverse x plus under root one minus x square plus c this is one way to do it that's another way to do it yeah we'll discuss all right you assume sin inverse x to be an angle theta that's another way to do it anyway have you copied this is that right so cos theta is cos x dx in your mind okay doesn't make much of a difference now this is behaving as an algebraic function this is behaving as a trigonometric function so which one will you take as u the algebraic function liat a comes first now apply integral of cos cos theta is sin theta minus theta the rule will be integral of du by d theta into integral v d theta over with respect to theta now very simple what is the sin theta minus cos theta so now please note you cannot leave us you so what is this you don't mind facing the camera which itself may be