Evaluate begin mathsize 12px style integral fraction numerator d x over denominator x to the power of 4 plus x squared plus 1 end fraction end style

Asked by sunil2791 | 17th Jun, 2017, 12:24: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator dx over denominator straight x to the power of 4 plus straight x squared plus 1 end fraction
straight x squared equals straight t
2 xdx equals dt
xdx equals dt over 2
rightwards double arrow integral fraction numerator dt over 2 over denominator straight t squared plus straight t plus 1 end fraction
Solve space using space completing space square space method.
NOTE colon
In space these space type space of space sums space you space have space to space convert space it space into space quadratic space equations space then
use space completing space square space method.
for space example space
integral fraction numerator straight x squared dx over denominator straight x to the power of 6 plus straight x cubed plus 1 end fraction
Here space we space have space to space convert space polynomial space into space quadratic space
then space put space space straight x cubed equals straight t rightwards double arrow 3 straight x squared dx equals dt
then space completing space square space method. end style

Answered by Sneha shidid | 17th Jun, 2017, 12:47: PM