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Integral Calculus

Blazing goIITian

Joined:	15 Nov 2009
Post:	608

11 Mar 2010 09:24:50 IST

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207

integrate the following

None

the answer happens to be ((x +root(a2 +x2 ))n )/n.............kindly post the solution

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सुपर मान

Hot goIITian

Joined: 7 Nov 2009

Posts: 199

11 Mar 2010 09:44:36 IST

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do it like this

take (x+(a^2 + x^2))^n=t

now diffrentiate and u will get

nt/(a^2+x^2)^1/2 dx = dt ...................(1)

put in the integral and get

integ. (t/(a^2+x^2)^1/2) ((dt(a^2+x^2)1/2 ) / nt) .................i.e. put value of dx interms of dt frm eq.1

now cancel out the terms and u will get the ans

if any step is unclear u can ask

Deepak Aggarwal

Blazing goIITian

Joined: 9 May 2009

Posts: 766

11 Mar 2010 10:14:34 IST

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Put y = x + (a² + x²)^1/2

So, dy = [ { x + (a² + x²)^1/2} / (a² + x²)^1/2 ] dx

or, dx / (a² + x²)^1/2 = dy / y

So, I = int y^n-1 dy = ( yⁿ / n ) + C = { (x + (a² + x²)^1/2)ⁿ / n } + C (Ans)

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