 Hi, and how are you all today? My name is Priyanka and I shall be helping you with the following question. It says integrate the following now We are given sine square 2x plus 5 here. We need to integrate it So let us start with our solution We need to integrate sine square 2x plus 5 Now we know that Sine square theta can be written as 1 minus Cos 2 theta divided by 2 right so on substituting 1 minus cos 2 theta by 2 in the function which is given to us where theta is 2x plus 5 we have 1 minus Cos 2 theta is 2x plus 5 divided by 2 dx Further we have Splitted the numerator and we have 1 by 2 minus cos 2 2x plus 5 divided by 2 dx Further this is equal to integral of 1 by 2 dx minus integral of cos 2 2x plus 5 divided by 2 dx now Here we have the constant will come out of the integral and we have left with integral of dx minus 1 by 2 integral of cos 2 2x plus 5 dx Here we have the answer as 1 by 2 integral of dx is x minus 1 by 2 integral of cos now here we can write Cos 2 2x plus 5 as integral of cos 2x sorry 2 theta will be equal to Here theta is 2x plus 5 Sine and theta can be written as 4x plus 10 divided by 4 plus C So we have Further the answer as x by 2 minus sin 4x plus 10 the whole divided by 8 plus C So this completes the session. This is the required answer. Hope you understood it well. Have a nice day