Integrate the following #int t/(t^4 +2) dt #?
2 Answers
Feb 19, 2017
Explanation:
Let
#I=1/2int(2tdt)/((t^2)^2+2)=1/2int(sqrt2sec^2thetad theta)/((sqrt2tantheta)^2+2)#
Continuing on and using
#I=1/sqrt2intsec^2theta/(2tan^2theta+2)d theta=1/(2sqrt2)intsec^2theta/sec^2thetad theta=1/(2sqrt2)intd theta#
We're working in terms of
#I=1/(2sqrt2)theta+C#
From
#I=1/(2sqrt2)tan^-1(t^2/sqrt2)+C#
Feb 19, 2017
I solved this way: