Question

`int(sin x)/(sin^(2)x+8)dx`​

Answer 1

Answer:

Step-by-step explanation:

Putting cosx+sinx=t in the integral

⟹(cosx−sinx)dx=dt

(cosx+sinx)  

2

=t  

2

 

⟹cos  

2

x+sin  

2

x+2sinxcosx=t  

2

 

⟹1+sin2x=t  

2

 

∫  

9−(1+sin2x)

​

 

dx

​

 

∫  

9−t  

2

 

​

 

dt

​

 

⟹sin  

−1

 

3

t

​

+C

⟹sin  

−1

 

3

1+sin2x

​

+C