Question

integrate dx / ((x^2) (sqrt(25-x^2))) using trig substitutions?

Answer 1

i think you use \(x=5\sin(u)\) so that
\[\sqrt{25-x^2}=\cos(u)\]

Answer 2

no that is wrong

Answer 3

\[\int\sin^2(u)^2\cos^2(u)du\]

Answer 4

what is u?

Answer 5

if you make the substitution
\[x=5\sin(u)\] the
\[u=\sin^{-1}(\frac{x}{5})\]

Answer 6

okay so what i did so far is replace x = 5sin u and dx=5cosu du

int 5cosu du/ 5sinu sqrt(25-(5sin^2 u))

sub y = sin u and dy = cosu du

dy/y^2 (5-u)