 Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says find the following integral that is integral of 1-x into root x dx. So let us start with the solution to this question. We have to find integral of 1-x into root x dx. This can be written as integral of root x minus x into root x dx. We have simply opened up the bracket. Now separating the terms we get integral of root x dx minus integral of x root x dx. Now we know that root x is same as x raise to power 1 by 2. So we can write integral of x raise to power 1 by 2 dx minus integral of. Now x into x raise to power 1 by 2 will be x raise to power 3 by 2 dx. Now this can be written as x raise to power 1 by 2 plus 1 divided by 1 by 2 plus 1 minus x raise to power 3 by 2 plus 1 divided by 3 by 2 plus 1 plus constant c. This happens because integral of x raise to power n dx is equal to x raise to power n plus 1 divided by n plus 1 plus a constant c where n is not equal to minus 1. Now n in the case of first integral is 1 by 2 and in the case of second integral it's 3 by 2. So we get this. On further simplification we get x raise to power 3 by 2 divided by 3 by 2 minus x raise to power 5 by 2 divided by 5 by 2 plus a constant c. Now this is equal to 2 by 3 into x raise to power 3 by 2 minus 2 by 5 into x raise to power 5 by 2 plus a constant c. So our answer to this question is 2 by 3 into x raise to power 3 by 2 minus 2 by 5 into x raise to power 5 by 2 plus c. So I hope that you understood the question and enjoyed the session. Have a good day.