Question

integrate t^2dt/(1+t^2)^1/2

Answer 1

familiar with hyperbolic functions ?

Answer 2

\[\large \int \dfrac{dx}{\sqrt{1+x^2}} = \sin h ^{-1}(x)+C\]

Answer 3

seen that before ?

Answer 4

no

Answer 5

Okay, then drop that idea, and you may work it using trig substitution

Answer 6

look at the stuff inside radical in the bottom

Answer 7

which trig substitution is appropriate here ?

Answer 8

tan

Answer 9

do it

Answer 10

ok

Answer 11

i am not getting

Answer 12

you may use tables also :

\[ \large \begin{align} \int \dfrac{t^2}{\sqrt{1+t^2}}~dt &= \int \dfrac{(1+t^2)-1}{\sqrt{1+t^2}}~dt \\~\\&= \int \sqrt{1+t^2}~dt ~-~\int \dfrac{1}{\sqrt{1+t^2}}~dt \end{align}\]

Answer 13

look up in your formulas,
you may find some formula for \(\large \int \sqrt{1+x^2} dx\)

otherwise use trig substitution and derive the formulas now

Answer 14

i got it thanks a lot

Answer 15

#29 and #32 formulas
http://integral-table.com/

Answer 16

yw :)