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1.integration of tan^-1(secx+tanx) 2.tan^-1(2cos^2theta/2-2-sin2theta)sec^2theta 2.integration of (1+2tanx(tanx+secx)^1/2

1.integration of tan^-1(secx+tanx)


2.tan^-1(2cos^2theta/2-2-sin2theta)sec^2theta


2.integration of (1+2tanx(tanx+secx)^1/2


 

Grade:6

3 Answers

vikas askiitian expert
509 Points
11 years ago

1) I=tan^-1secx+tanx)dx

secx+tanx=1+sinx/cosx

 1+sinx=(sinx/2+cosx/2)^2

   cosx=(cosx/2-sinx/2)(cosx/2+sinx/2)                    

 I=tan^-1(sinx/2+cosx/2)/(cosx/2-sinx/2)dx

   =tan^-(tanpi/4+x/2)dx

   =(pi/4+x/2)dx =(pi/5)x + x^2/4 +k

2)I=(1+2tanx(tanx+secx)^1/2dx

     =(1+tan^2x + tan^2x +2secxtanx)^1/2 dx

     =( sec^2x +tan^2x +2tanxsecx)^1/2dx

     = ((secx+tanx)^2 )^1/2dx

    =  ( secx+tanx )dx

     =logsecx+tanx  +logsecx +c

    =log(secx+tanx)secx  +c

 

 

 

aman bansal
askIITians Faculty 33 Points
10 years ago

=tan-1(1+sinx/cosx)

=tan-1((sinx+cosx)2/(cosx2-sinx2))

=tan-1(tan(x+∏/4)

=x+pi/4

ankit singh
askIITians Faculty 614 Points
one year ago

I=integ.of. tan^-1(1+sinx)/cosx.dx

I=integ.of. tan^-1(cos^2x/2+sin^2x/2+2.sin x/2.cos x/2).dx /(cos^2x/2-sin^2x/2)

I=integ.of tan^-1(cos x/2+sin x/2)^2.dx/(cos x/2+sin x/2).(cos x/2-sin x/2).

I=integ.of tan^-1(cos x/2+sin x/2).dx/(cos x/2-sin x/2).

I=integ.of tan^-1 (1+tan x/2)/(1-tan x/2).dx

I=integ.of tan^-1 (tanπ/4+tan x/2)/(1-tan π/4.tan x/2).dx

I=integ.of tan^-1 tan (π/4+x/2).dx

I=integ.of. (π/4+x/2).dx

I = π/4. x. +x^2/(2.2). +C

I= π.x/4. +x^2/4. +C. Answer.

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