IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

apurviitjee2008

_{0[ ]}

^{[infinty ]} x³+3/x⁶(x²+1)=

(a+b

)/c

find a b and c

experts plz help me with this problem

apurviitjee2008

anyone plzzzzzzzz

apurviitjee2008

experts help plz!!!!!!!!!

nivedh_89

hey apoorva..................!!!!!!!!!!!!!!!!!!!
use this formula.................!!!!!!!!!!!!
maybe it will help.................!!!!!!!!!!!!!!!!!!!!

: $displaystyle intdisplaystyle rac{dx}{x^{displaystyle m}(x^{displaystyle2... ...x^{displaystyle m-2}(x^{displaystyle2}+a^{displaystyle2})^{displaystyle n}}$

iitkgp_bipin

Substitute x = tany
dx = sec²y.dy

I =

[(tan³y + 3) / {tan⁶y.(tan²y+1)}].(sec²y..dy)

I =

[(tan³y + 3) / (tan⁶y.sec²y)].(sec²y..dy)

I =

(tan³y + 3) / (tan⁶y). dy

I =

coty³y.dy + 3(

tan³y.dy)

coty³.dy

=

coty.cot²y.dy

=

coty.(cosec²y - 1).dy

=

coty.cosec²y.dy -

coty.dy

= -

coty.d(coty) -

d(sinx)/sinx

= -cot²y/2 - ln(sinx) + c

Similarly proceed for 3(

tan³y.dy).

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