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Discussion Response Post to: integration problem

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Priyesh (1601)

Blazing goIITian

total posts: 1042
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Hi gonik

see

_{[ ]}^{[ ]} (x^3m+x^2m+x^m)(2x^2m+3x^m+6)^1/mdx

= _{[ ]}^{[ ]} (x^3m-1+x^2m-1+x^m-1)(2x^3m+3x^2m+6x^m)^1/mdx (by taking x out from first bracket expression & putting it inside second bracket expression)

now put (2x^3m+3x^2m+6x^m) = t^m

=> 6m(x^3m-1+x^2m-1+x^m-1)= mt^m-1dt

=> therefore the first bracket expression in the integral along with dx becomes

1/6 t^m-1dt

therefore the integral becomes

1/6_{[ ]}^{[ ]} tt^m-1dt = 1/6_{[ ]}^{[ ]} t^mdt

therefore the ans(in terms of t) is 1/6 t^m+1/(m+1)

now substitute back value of t to get the ans. in terms of x

this question first came in a russian olympiad & then came in IIT-JEE.

hope you understood

cheers!!!!!!

"Imagination is more important than knowledge."

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