INTGRATION OF COSEC(X) USING SUBSTITUTION MEHTOD

Here is the step-by-step solution to integrate cosec(x) dx using the substitution method: 

∫ csc(x)dx

= ∫(cscx−cotx)cscx(cscx−cotx)​dx         ( multiplying by cscx−cotx in numerator and denominator)

assume, u= cscx−cotx

du =  (−cscxcotx+csc2x)dx

dx=−cscx(cscx−cotx)du

= ∫cscx−cotxcscx(cscx−cotx)​.(cscx−cot
x)(cscx)du​

=∫
du​u=log∣u∣+C

∴∫cscxdx=log∣cscx−cotx∣+ C.        (Placing value of  u )