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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
```
7 years ago

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
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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