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r Grade: 6
        

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


 

7 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

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


 


 


 

7 years ago
aman bansal
askIITians Faculty
33 Points
										

=tan-1(1+sinx/cosx)


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


=tan-1(tan(x+∏/4)


=x+pi/4

7 years ago
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