" The value of "(int_(0)^(1)(dt)/(sqrt(1-t^(4))))/(int_(0)^(1)(1)/(sqrt(1+t^(4)))dt)" is "

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int_(0)^(1)t^(5)*sqrt(1-t^(2))*dt

int_(0)^(1)t^(2)sqrt(1-t)*dt

I=int_(0)^(-1)(t ln t)/(sqrt(1-t^(2)))dt=

int(dt)/( sqrt(1-t)-t)

int(1)/(sqrt(t)+1)dt

" (a) "int(dt)/(sqrt(1-t^(2)))

int(1)/(sqrt(t))dt

The value of int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t)dt is

int(dt)/( sqrt(t-1))