Question

how do you find the antiderevative of 1/sqrt(x+1)

Answer 1

using substitution

Answer 2

\[\int{\frac{1}{\sqrt{x+1}}}dx = \int{(x+1)^{-\frac{1}{2}}}dx\]
\[u := x+1\]
\[du = dx\]
\[\implies \int{u^{-\frac{1}{2}}}du = 2\sqrt{u} = 2\sqrt{x+1}\]

Answer 3

let:
u=x+1 and du=dx
\[\int \frac{1}{\sqrt u}du=2\sqrt u +C= 2\sqrt {x+1}+C\]

Answer 4

damn I forgot the C... the C!!!!

Answer 5

silly constants!

Answer 6

I never remember the C

Answer 7

You shouldn't have to write C. It should be implied