Question

integral (x^2)/((4-x^2)^(3/2))dx

Answer 1

@surjithayer why does it take too long to type?? hehehe

Answer 2

\[I=-\int\limits \frac{- x^2+4-4 }{\left( 4-x^2 \right)^{\frac{ 3 }{ 2 }} }dx\]
\[=-\int\limits \frac{ 4-x^2 }{ (4-x^2)^{\frac{ 3 }{ 2 }} }dx+4 \int\limits \frac{ 1 }{ (4-x^2)^{\frac{ 3 }{ 2 }} }dx\]
\[=-\int\limits \frac{ dx }{ \sqrt{4-x^2}}+4I1+c=-\sin^{-1} \left( \frac{ x }{ 2 } \right)+4I1+c\]
for I1 put x=2sin theta and complete.

Answer 3

Woahh... ...excellent solution to me.

Answer 4

sorry for late . i typed twice but some how i failed to post.

Answer 5

thank you!