plz give sum hint!!!

AIEEE 2015 Guidance › Calculus questions › plz give sum hint!!!

1. âˆ«cos²x/ (1+tanx) dx
2. âˆ«[(x/e)^x+(e/x)^x] lnx dx

#Mathematics #Calculus

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6 Answers

1357

Manish Shankar ·2009-07-22 03:59:26

1.
cos²x/(1+tanx)=sec²x/[sec⁴x(1+tanx)]=sec²x/[(1+tan²x)²(1+tanx)

I don't have any better approach

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1357

Manish Shankar ·2009-07-22 04:27:27

2.
[(x/e)^x+(e/x)^x]lnx=(x/e)^xlnx+(e/x)^xlnx
taking first one
(x/e)^xlnx dx

taking (x/e)^x=t

then (x/e)^xlnx dx=dt

âˆ«(x/e)^xlnx dx=âˆ«dt=t+C=(x/e)^x+C

Similarly fond for other

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11

Devil ·2009-07-22 05:45:34

2nd one can be esily killed by parts.

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341

Hari Shankar ·2009-07-22 07:01:58

http://www.goiit.com/posts/list/integration-integration-plz-can-anyone-help-me-77629.htm#379975

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1

Surbhi Agrawal ·2009-07-22 08:39:16

can u explain the first one!.. i got the 2nd one!!

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11

Mani Pal Singh ·2009-07-22 09:00:01

In the 1st u have to know that d/dx tanx =sec²x
so

multiply num and denom by sec⁴x

upper sec²x and neeche sec⁴x+tanxsec⁴x aa jaega

then put tanx=t and sec²xdx=dt

neeche sec⁴x ko write in terms of tan x and substitute to get ur answer

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