How do you integrate by substitution $int tsqrt(t^2+2)dt$ ?

Question

2195 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-17T13:56:03

The answer is $=(t^2+2)^(3/2)/3+C$

Let $u^2=t^2+2$

Differentiating both sides

$2udu=2tdt$ , $=>$ , $tdt=udu$

Therefore,

$inttsqrt(t^2+2)dt=intu*udu$

$intu^2du=u^3/3$

$=(t^2+2)^(3/2)/3+C$

How do you integrate by substitution int tsqrt(t^2+2)dtint tsqrt(t^2+2)dt?