00:01
Let's have a look at the question.
00:03
So here we have to integrate the integral integration of sec to the power 4, 5x, multiplied by tan to the power 4 5x dx.
00:19
So here first of all, let us substitute the value of 5x is equals to you.
00:29
Now, differentiating u with respect to x, we will get 5.
00:36
So therefore, from here we can write that dx is equals to 1 upon 5 d .u.
00:44
So now, our integral will become 1 upon 5 integration of sec to the power 4 u and multiplied by tan to the power 4 u.
01:01
Now we will be using sec square u is equals to tan square u plus 1.
01:12
So here now let us put the value.
01:15
So we will get 1 upon 5 integration of sec square u into tan to the power 4 u and into tan square u plus 1 d u...