 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says integrate the following function that is sin inverse x the whole square. So let us see the solution to this one. We have to find i that is equal to sin integral of sin inverse x the whole square dx. First of all we put sin inverse x equal to theta. This implies that x is equal to sin theta and this implies that dx is equal to cos theta d theta. Therefore i becomes integral theta square into cos theta d theta. Now we integrate this by paths. So we see that this is the first function. This will be the second function because as per the i-late rule, algebraic function is given preference over trigonometric function. So that will be equal to first function into integral of second function that is cos theta d theta minus integral of d by d theta of theta square that is of the first function into integral cos theta d theta into d theta. This is equal to theta square into integral of cos theta d theta is sin theta minus d by d theta of theta square is 2 theta and integral cos theta d theta is sin theta this into d theta. This is equal to theta square sin theta minus 2 into integral theta sin theta d theta. Now here again we apply integration by paths. So this will be first function, this will be the second function. We get theta square sin theta minus 2 into theta into integral of sin theta d theta is minus cos theta minus integral of d by d theta of theta that is 1 into integral of sin theta is minus cos theta d theta plus some constant c this is equal to theta square sin theta plus 2 theta cos theta minus minus become plus. So we have a minus sign here also so we will have minus 2 integration cos theta d theta plus c this is equal to sin theta d theta is equal to theta square sin theta plus 2 theta cos theta can be written as square root of 1 minus sin square theta minus 2 sin theta because integration of cos theta is sin theta. So minus 2 sin theta plus the constant c now converting it back to x we know that theta was equal to sin inverse x so we have sin inverse x the whole square into sin theta that is x plus 2 into sin inverse x into square root of 1 minus x square minus 2 x plus c. So this is our answer to the question I hope that you understood the question and enjoyed the session have a good day.