Question

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

Answer 1

[ t sqrt ( t ) + t sqrt ( t ) ] = 2 t sqrt ( t )


2 t sqrt ( t ) / t ^ 2 = 2 * sqrt ( t ) / [ sqrt ( t ) * sqrt ( t ) * t ] =

2 / sqrt ( t ) = 2 * t ^ ( - 1 / 2 )


int [ 2 * t ^ ( - 1 / 2 ) ] dt =

2 * t ^ ( - 1 / 2 + 1 ) / ( - 1 / 2 + 1 )=

2 * t ^ ( 1 / 2 ) / ( 1 / 2 ) =

2 * 2 * sqrt ( t ) = 4 sqrt ( t ) + C

Answer 2

I think you forgot the extra t in the denominator at

2 / sqrt ( t ) = 2 * t ^ ( - 1 / 2 )

Should be

2t^(-3/2)

and proceed from there...