Examples : Integration by Partial Fractions Part 2 Video Lecture | Mathematics for GRE Paper II

hello friends this video on integrals
part 28 is brought you by exam feel calm
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this video please make sure that you
have watched part 1 to power 27 it's all
this question first begin your spatula
this becomes X / - 1 into X square plus
1 for the factorize the scales becomes 1
by X minus 1 into X plus 1 dou X square
plus 1 this kind of factor we have tried
in this form V by X minus 1 plus V by X
plus 1 plus C X plus T bar x squared
husband why because this is X square
plus first not for the frequency now we
define the value of ABC and D so what we
can do you can do write like this this
guy becomes X we powerfulness 1 and this
becomes a into X plus 1 into X square
plus 1 right plus B into X minus 1 into
X square plus 1 plus C X plus B into
thanks very much correct now I have to
find the value of these things right a B
C and E I have to approach analyze equal
to 1 by X for 4 months so I can either
keep putting the values X is equal to 0
X is equal to 1 right that kind of thing
but I can solve this I will get the
coefficient of x cube X square those
kind of things right and then I can
equate the values for example if I saw
this further I get the coefficient of x
t mass a plus B plus C and X square as
minus a plus B plus D and X as a plus B
minus C and some constant iners minus a
plus
last right this by actually pod one
minus one is going to do 1 by X is equal
work you compare the coefficient of x
here is 0 so I can write first equation
and the lights over here a plus B plus C
similarly this guy of 0 coefficient of x
square I can write minus a plus B plus B
coefficient of x da 0 so it was B plus C
of 0 and this is 1 actually so I can
write minus a plus B minus so we solve
these we saw these equations right
taking two each time right so what you
can get is this is minus so what you get
is you have a you take these two
equation right a plus B plus C 0 NE + B
minuses to enjoy if you add both pain
you can see it's better right you add
these two you could see is equal to 0
and E Plus be also 0 right this is easy
the rezident a plus B equals 1 and then
we keep swallowing and get a is equal to
minus 1 where all B is equal to 1 by n
minus 1 that is what it is it's all for
this will get to the palace so now this
is I can write integral of x to the
power 4 minus 1 DX has nothing but minus
1 by 4 integral of X minus 1 DX plus V
that is 1 by 4 1 by X plus 1 correct yes
plus CX Plus D is C 0 X plus D is minus
1 by 2 integral of 1 by X square plus 1
right now finding is easy how this guy
is nothing but 1 by 4 log of X minus 1
this guy is nothing but 1 by 4 log of X
plus 1 and this guy is nothing
you see tan universe 6 if you seek one
by full common this becomes log of X
plus 1 by X minus 1 minus 2 and Muslims
and there's münster so it was not that
difficult question the only thing it was
I have to convert this guy into this X a
by X minus 1 B by X plus 1 and C by C X
plus D by X square plus 1-form hi in the
hollow of ABC and advance let's see what
will happen if I get this kind of
equation X to the power n plus 1 and X
this kind of equation if you see the
only thing I have is I can put this guy
as n H to the power n is printed deep
sorry it's too bad until T or I get n X
to the power n minus 1 DX is equal to D
Phi at DX has nothing burned DT by H to
the power n minus 1 and destroy correct
so if this dot DX is I have to find DX
becomes DD by n X to the power n minus 1
into things that this becomes deeply
I'll let me assume this is T plus 1 so
this plus 1 is going to be you steal
anything is fine actually if I assume
this guy as 40 is okay okay notice in
this they are the S T X to the power n
guilty so this is T plus now if you
observe this carefully this is nothing
but n X to the power n in to eat the
snow and ice to the power n is again T I
know he was nothing but DT by n T into T
plus 1 correct since n is constant I can
see that is nothing but 1 by n
one by T plus one Leedy correct so what
we have seen there this such a complex
thing is divided into a simpler form now
why simpler form because one by T into 1
by T plus 1 I can just write this guy as
a by T plus B by P plus 1 correct
you saw the values of a and B I think
you'll get a is 1 and B is minus 1 so
the same thing I can write as 1 by n
into 1 by D plus minus 1 by T plus 1 D D
and there is nothing but 1 by n 1 by T
DT minus 1 by n again constant 1 by D
plus 1 D D correct this is nothing but 1
by n my constant log of e minus log of P
plus 1 correct and this is nothing but 1
by n log o T by T plus 1 never the value
of D actually fallen so this becomes log
of X to the power n by X to the power n
plus 1 and plus constant is maths we
have to add constant so what is it in
this case we have used substitution plus
partial fractions to solve this question
so we don't use only one method
sometimes we use multiple methods
example multiple tools that you saw in
this case we use first to use the
substitution method you convert it into
simpler from little simpler form and
then we use partial fraction to them why
do fools simple form and then we got the
answer
thank you
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