Question

∫cosecxdx is equal to:​

Answer 1

Answer:

I=∫cscxdx

⇒I=∫  

(cscx−cotx)

cscx(cscx−cotx)

​  

dx

Put cscx−cotx=t

⇒(−cscxcotx+csc  

x

x)dx=dt

⇒dx=  

−cscx(cscx−cotx)

dt

​  

 

⇒I=∫  

cscx−cotx

cscx(cscx−cotx)

​  

.  

(cscx−cot  

2

x)(cscx)

dt

​  

 

        =∫  

t

dt

​  

=log∣t∣+C

∴∫cscxdx=log∣cscx−cotx∣+C

Step-by-step explanation:

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