Question

integrate arcsin[x] / sqrt[1+x]

Answer 1

integration by parts

u = arcsin dv = 1/sqrt(1+x)

du = 1/sqrt(1-x^2) v = 2sqrt(1+x)

\[\int\limits u dv = u v - \int\limits v du\]
\[= 2 \sin^{-1} (x) \sqrt{1+x} - 2 \int\limits \frac{dx}{\sqrt{1-x}}\]
...

Answer 2

thank you, i had my parts flipped to what you have; which complicated it more then simplify :)

Answer 3

http://www.wolframalpha.com/input/?i=integrate+arcsin%28x%29+%2F+sqrt%281%2Bx%29

Answer 4

Just to verify your answer
\[
\int \frac{\sin ^{-1}(x)}{\sqrt{x+1}} \, dx=\frac{2 \left(2 \sqrt{1-x^2}+(x+1) \sin
^{-1}(x)\right)}{\sqrt{x+1}} + C
\]