 Hello and welcome to the session. Let us discuss the following question. Question says, integrate the function sin inverse x upon square root of 1 minus x square. Let us now start with the solution. Now we have to integrate sin inverse x upon square root of 1 minus x square with respect to x. Clearly we can see derivative of sin inverse x is also occurring in this integrand. So we will integrate this function by a substitution method of integration. We make a substitution for a function whose derivative also occurs in the integrand. So we will substitute sin inverse x is equal to t. Now we can write put sin inverse x is equal to t. Now differentiating both the sides with respect to x we get 1 upon square root of 1 minus x square is equal to dt upon dx. Now this further implies 1 upon square root of 1 minus x square dx is equal to dt. Now we can write integral of sin inverse x upon square root of 1 minus x square dx is equal to integral of t dt. We know sin inverse x is equal to t. So we can substitute t for sin inverse x here and dx upon square root of 1 minus x square is equal to dt. So here we have substituted dt for dx upon square root of 1 minus x square. Now integrating this function we get t square upon 2 plus c where c is the constant of integration. We can find integral of this function by using the formula of integral of x raised to the power n with respect to x. This is equal to x raised to the power n plus 1 upon n plus 1 plus c where c is the constant of integration. Here the value of n is 1. So integral of this function is equal to t raised to the power 1 plus 1 upon 1 plus 1 and we know 1 plus 1 is equal to 2. So we get t square upon 2 plus c. Now we know t is equal to sin inverse x. So we get square of sin inverse x upon 2 plus c. So required integral of the function sin inverse x upon square root of 1 minus x square is equal to sin inverse x square upon 2 plus c. Or we can write it as 1 upon 2 multiplied by square of sin inverse x plus c. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.