00:01
Let's evaluate this integral.
00:03
We have the expression 8 tangent power 4x, second power 6x dx.
00:08
So first we are going to rewrite this integral expression.
00:12
First i factor the 8 out of the integral and then write this as tangent power 4x.
00:18
I'm now going to write the 2nd 6x as product of 2nd power 4x times 2nd squared x.
00:28
Basically we split this second power 6x as a product of two second function as like this now in the next step i'm going to do one more relating that is this will become tangent power 4x now we can write this as second squared x quanti squared and then multiply this with second squared dx let's consider this as a group so i put bracket now in the next step i'm going to use pythagorean identity for second squared x.
01:01
We know the pythagorean identity 1 plus tangent squared x equals second squared x.
01:09
So we can replace the second square x basically as 1 plus tangent squared x.
01:14
So therefore this will become tangent power 4x times i'm replacing the second squared x as 1 plus tangent squared x and this is quantity square.
01:26
Then we have a sequence squared x d x now we can integrate this using u substitution so i'm going to put tangent x this equals u and this implies tangent power 4 x is u power 4 also tangent squared x equals u squared let's also find the derivative the derivative of tangents x is second squared x d x and this equals the derivative of u is to you, which means in our original integral, we can replace this as the u.
02:09
And wherever we have tangent x, we replace that by u.
02:13
And so therefore, this will become u power 4 because tangent power 4x is u per 4...