\int (x^{2}+2x + 3)\sqrt{x^{2}+x+1}dx
please help. ans nahin pata mujhe...
full soln. hi likhiyo.
aur haan dekhene walon sirf dekho maat try karo aur post the soln.
1write
x^2 + 2x + 3 as
m ( x^2 + x + 1) + n \frac{d\left(x^2 + x + 1 \right)}{dx} + u
evaluate m , n, u
u get
m = 1
n=1/2
u = 3/2
integral reduces as
{\color{blue} \int\left[ \left(x^2 + x +1 \right) + \frac{1}{2} ( 2x + 1) + \frac{3}{2}\right]\sqrt{x^2 + x +1} . dx }
convert these into perfect squares and use formula for
now use the formula
{\color{blue} \int \sqrt{x^2 + a^2} . dx }
and done
1kaise please elaborate.
perfect squares kaise karoon. full soln .please.
39The term
is giving hyperbolic arcsin. That shouldn't happen...the next two terms are integrable as per our syllabus but I don't think this one is...if there is any other way to do it I'd love to know.