 Hello and welcome to the session. My name is Mansi and I am going to help you with the following question. The question says, find the following integral. That is, x cube plus 5x square minus 4 divided by x square dx. So let us start with the solution to this question. Now we are given integral of x cube plus 5x square minus 4 divided by x square dx. This can be written as integral of x cube by x square plus 5x square by x square minus 4 by x square dx because we have taken x square in the denominator with each term in the numerator. Now this can be separated and written as integral. Now x cube divided by x square is x. So it is x dx plus x square gets cancelled with x square. So 5 integral of dx minus 4 into integral of 1 by x square dx. Now this can be written as x square by 2 plus 5 into x minus 4 into x raise to power minus 2 plus 1 divided by minus 2 plus 1 plus a constant c that is equal to x square by 2 plus 5x plus 4 by x plus c. Now this we get because we know that integral of x raise to power n dx is equal to x raise to power n plus 1 divided by n plus 1 plus c where n is not equal to minus 1. So in the first integral we see that n is equal to 1. So we will get x raise to power n plus 1 that is 2 divided by n plus 1 that is 2. In the second integral we see that it is equivalent to say that we have a 1 here. 1 is written as x raise to power 0. So n becomes 0 in this case and we get x raise to power 1 divided by 1 minus 4 into x raise to power minus 2 plus 1 because n in this case is minus 2. So we get this on simplification. So our answer to this question is x square by 2 plus 5x plus 4 by x plus c. So I hope that you understood the question and enjoyed the session. Have a good day.