Question

TU
7. tan
= tan x + sec X
+
N18
4.​

Answer 1

Answer:

Step-by-step explanation:

∫(1+2tanx(secx+tanx)  

2

1

​  

 

dx

=∫(1+2secxtanx+2tan  

2

x)  

2

1

​  

 

dx

=∫(1+tan  

2

x+tan  

2

x+2secxtanx)  

2

1

​  

 

dx

=∫(sec  

2

x+tan  

2

x+2secxtanx)  

2

1

​  

 

dx

=∫(secx+tanx)  

2

2

​  

 

dx

=∫(secx+tanx)dx

=∫(secxdx)+∫(tanxdx)

=ln∣secx+tanx∣+ln∣secx∣+C

=lnsecx(secx+tanx)+C