Question

1/((sqrtx)(sqrtx+1)) dx integral

Answer 1

is it (sqrtx +1) or sqrt(x+1)?

Answer 2

\[1/((\sqrt{x})(\sqrt{x}+1))\]

Answer 3

the answer from the book is\[2\ln \left| \sqrt{x}+1 \right|+c\]

Answer 4

this is equal to

dx/(x + sqrtx) . let u = sqrtx so du = 1/2 (x^(-1/2)) * dx

this is equal to [1/(u^2 + u)] * 2u du

= 2u/(u^2 + u)

lmk if you would like the next step

Answer 5

ok i substituted sqrtx back in but its not the book answer

Answer 6

ooh the book say use (sqrtx+1)=u

Answer 7

2u/(u^2 + u) = 2/(u +1) --> simpler to integrate

Answer 8

both substitutions work. in fact even a whacky substitution like u = sqrtx + pi could work if done right.

integral is 2 ln |u + 1| + C . u = sqrtx.

^_^

Answer 9

thanks you so much for helping me