IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

ckr

INREGRAL OF (x^2 + 2x)/log(x+1) (limit is -1 to 0 )

priyesh

aman23iit

hi friend it was an exelent Q

here it is

apply

F(a+b-x)dx=

F(x)dx also put x=-h

you will get

1-h²/logh.dh limit 0-1

now take e^y=h you will get

_{[-infinite ]}

^{[0 ]} e^y/y.dy -_{[-infinite ]}^{[0 ]}e^2y/y.dy--------- multiply this with 2 and divide also

and take 2y=z in second part

you will get the value =0

bye

plz rate me as i am new

shakirshafi12

well the answer is not 0 for sure
this question was posted by magiclko and the answer of this question is ln3
and not zero

t_c511

(x^2 + 2x)/log(x+1)

_{[-1 ]}

^{[0 ]} [(x+1)² - 1] / ln(x+1)
Put x+1 = t and then again replace t as x
_[0]

^{[1 ]} [x² - 1] / ln | x |
put 2 as

let it be a function of

f(

) = _{[0 ]}

^{[1 ]} [x - 1] / ln | x | ..........( 1 )
now differentiate w.r.t to

treating x as constant
we get,
f '(

) = _[0]

^{[1 ]} [x ln x]/ ln x
f ' (

) = _{[0 ]}

^{[1 ]} x

f ' (

) = x⁺¹ /

+1 ...... 0 to 1
= 1/

+1
f (

) = ln (

+1) + c .........integrating indefinitely
we know that from (1) f (0) = 0 therefore c = 0
f(

) = ln(

+1)
resubstituting

= 2, we get
f (2) = ln 3

cheeers

pls guys RATE for this i'm a newbie here