 Hello and welcome to the session. Let us discuss the following question, question says, find the following integrals. We have to find the integral of root x minus 1 upon root x whole square dx. First of all, let us understand that k1 f1 x plus k2 f2 x plus k3 f3 x plus kn fn x dx is equal to k1 multiplied by integral of f1 x dx plus k2 multiplied by integral of f2 x dx plus k3 multiplied by integral of f3 x dx plus kn multiplied by integral of fn x dx. Now in this expression, k1 k2 k3 till kn are real numbers and integral of dx is equal to x plus c, where c is the constant of integration. Also integral of x raise to the power n dx is equal to x raise to the power n plus 1 upon n plus 1 plus c, where c is the constant of integration. Let us now start with the solution. Now we have to find the integral of root x minus 1 upon root x whole square dx. Now this integral can be further written as integral of square of root x plus square of 1 upon root x minus 2 multiplied by root x multiplied by 1 upon root x. We know a minus b whole square is equal to a square plus b square minus 2 multiplied by a multiplied by b. Now this integral can be further written as integral of x plus 1 upon x minus 2 dx. We know square of square root of x is equal to x and square of 1 upon root x is equal to 1 upon x and this root x and this root x will get cancelled and we get 2 here. Now using expression 1 of the key idea we can write this integral as integral of x dx plus integral of 1 upon x dx minus 2 multiplied by integral of dx. Now from key idea we know integral of x raise to the power n is equal to x raise to the power n plus 1 upon n plus 1. Here value of n is 1. So integral of x dx is equal to x raise to the power 1 plus 1 upon 1 plus 1 plus integral of 1 upon x is log x and integral of dx is x. So we will write here 2x and c is the constant of integration. Now this is further equal to x square upon 2 plus log x minus 2x plus c. So our required answer is integral of root x minus 1 upon root x whole square dx is equal to x square upon 2 plus log of x minus 2x plus c where c is the constant of integration. This completes the session. Hope you understood the solution. Take care and have a nice day.