IIT JEE , AIEEE Forum - Mathematics , Integral Calculus - Integrate

srujana

$\int\left(x^2+2x+3\right)\sqrt{x^2+x+1}\ .dx$

Ans: Click here

anandghegde

You want only that ans or will you accept other answers too?

anandghegde

isnt this a standard kind of prob?

srujana

Any right ans / genuine attempt is accepted ! :)

(P.S- shd have least poss no of steps)

srujana

is it??

(forgive me if it is!...m a beginner at integration..!)

anandghegde

Write the integral as $\int [ (x+ \frac{1}{2})^2 + (\frac{\sqrt{3}}{2})^2)^{\frac{3}{2}} dx$ $\frac{1}{2} \int (2x-1) \sqrt{x^2+x+1} dx$

$+ \frac{3}{2} \int \sqrt{(x+ \frac{1}{2} )^2 +(\frac{ \sqrt{3}}{2})^2} dx$

now proceed

srujana

It more or less resembles my procedure....which no doubt isnt that short...

it gives the ans

$I=\frac{9}{64}sec^3\theta tan\theta+\frac{27}{128}sec\theta tan\theta +\frac{27}{128}ln|sec\theta +tan \theta|+....some\ crap\\$

$whr\ tan\theta =\left(\frac{2x+1}{\sqrt{3}}\right)$

(which no way resembles the given ans)

anandghegde

you want the answers to tally with those given by mathematica?

sandeepramesh

There might be many ways of integrating the expression! By no means need all the answers tally!

srujana

hey ppl...!

atleast try completing the sum...

(note the word completing..!)

n as i have said...m luking fr any "simple trick" which these kind of qs usually have to crack them n leave ppl surprised !

anandghegde

no simple trick......this is a standard prob

of this type

$\int (px^2+qx+r) \sqrt{ax^2+bx+c} dx$

sandeepramesh

maybe it helps if you know what on integrating gives sinh^{-1} function thats all

sboosy

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