00:01
All right here, we need to evaluate the integral, right? so let us say this is i is equal to integration of, integration of 1 by root x multiplied by 4 plus x, right? this is what we have.
00:30
Right, so this is dx.
00:32
Let's understand it.
00:34
So first of all, you will assume let you is equal to root.
00:39
X right this is equal to when you uh write it as u square is equal to x right so which means that d x would be equal to what d x is equal to do you do d u right and uh root x is equal to u itself right this is what we know uh okay so now you can plug in this value here right so can do you can write it as i is equals to integration of 1 upon u plus u multiplied by this is u multiplied by u multiplied by 4 plus u square yes this is what we have now d x could be replaced as 2 u d u yes so this becomes equals to 2 by this becomes 2 multiplied by 1 by uu cancels out each other, right? so 1 by 4 plus u square, right? so this is du here.
01:54
Perfect.
01:55
Now we know a relationship here, right? so the integral now has the standard form, right? since we know here, since integration of 1 upon a square plus u square is equal to, a square plus u square is du is equal to what? it would be equal to 1 upon a tan inverse u by a plus c.
02:26
So this is the integration we know...