00:01
The integral is given as integration with boundaries pi 0 1 by 1 .25 plus cos w dw.
00:08
So, this is equation 1.
00:10
Now, equation 1 can be written as i is equal to integration with boundaries pi 0 1 by 5 by 4 plus cos w dw since 5 by 4 is equal to 1 .25.
00:27
So, i will be equal to integration with boundaries pi 0 4 by 5 plus 4 cos w dw and i will be equal to 4 into integration with boundaries pi 0 1 by 5 plus 4 cos w dw.
00:44
Next i will be 4 integration with boundaries pi 0 1 by 5 plus 4 into 1 minus tan square w by 2 divided by 1 plus tan square w by 2 dw since cos 2x is equal to 1 minus tan square x divided by 1 plus tan square x.
01:10
So, this will be 4 integration with boundaries pi 0 1 by 5 into 1 plus tan square w by 2 plus 4 into 1 minus tan square w by 2 whole divided by 1 plus tan square w by 2 dw.
01:34
So, this will be 4 integration with boundaries pi 0 1 plus tan square w by 2 divided by 5 plus 5 tan square w by 2 plus 4 minus 4 tan square w by 2 dw.
01:51
So, the integral will be 4 integration with boundaries pi by 0 sec square w by 2 divided by 9 plus tan square w by 2 dw.
02:05
This is equation 2.
02:07
Put tan w by 2 is equal to t and differentiate equation 2.
02:17
So, we get d by dw tan w by 2 is equal to dt.
02:24
So, sec square w by 2 into 1 by 2 dw is equal to dt...