Solve `int``(2x)/(1+x^2)` `dx`

Answer

A

Explanation

`r'(t)=-2hati+2thatj+4e^(2(t-1))hatk`
since, `r'(t)` is parallel to r(t),
so `r(t)=alphar'(t)`
`1-2t=-2alpha,t^(2)=alphat,2e^(2(t-1))`
`=4alphae^(2(t-1)),alpha=(1)/(2)`
the only value of t which satisfies all three equations is t=1.
so, r(1) is the required point (-1,1,2).