00:01
Hi, there is a question in this time to evaluate the integral minus 10 divided by x minus 1 and x square plus 9 dx.
00:12
Let us write it as i and i will be using the partial fraction and before that minus 10 let us write 1 by x minus 1 x square plus 9 dx.
00:26
I will be using partial fraction over here.
00:29
So 1 by x minus 1 x square plus 9, let us say a by x minus 1 as this is linear and b by this is quadratic.
00:41
So x square plus 9 and bx plus c.
00:47
That means a into x square plus 9 plus bx plus c into x square x minus 1 divided by x minus 1 x square plus 9.
00:58
These two gets cancelled out.
01:01
So 1 equal to a into x square plus 9 plus bx plus c into x minus 1.
01:13
Now i need to find the values of a, b and c.
01:16
So let us compare the coefficients of x square x and constant.
01:24
So a plus b, this is x square and if you multiply it will be cx minus bx.
01:32
So c minus bx plus 9a minus c.
01:40
One, after comparing a plus b will become equal to 0 because there is no x square here.
01:48
Second is c minus b equal to 0.
01:52
So c equal to b.
01:53
Third is 9a minus c equal to 1.
02:01
So let us plug in c equal to b over here.
02:05
9a minus b equal to 1.
02:08
9a minus b equal to 1.
02:11
Adding, it will be 10a equal to 1...