Thursday, April 28, 2016

Evaluate the integral


Let's evaluate the above integral by rewriting the integrand as,





Now again rewrite the second integral,




Now let's evaluate the above three integrals,



Let's use the integral substitution,


Let u=x-1,


du=dx



The above can be evaluated using the standard integral,





Substitute back u=x-1,



Now let's evaluate the second integral by integral substitution,



Let 







Substitute back 



Noe let's evaluate the third integral,




Let's use the integral substitution,


Let 




Using the identity:





Now use the identity:






Substitute back 







Add a constant C to the solution and simplify,



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