Investigate the following improper integrals for convergence :
(a) `int_(0)^(1)(e^(x)dx)/(sqrt(1-x^(3))),`
(b) `int_(0)^(1)(x^(2)dx)/(root3((1-x^(2))^(5))),`
(c ) `int_(0)^(1)sqrt((x)/(1-x^(4)))dx,`
(d) `int_(0)^(1)(dx)/(1-x^(3)+x^(5)),`
(e ) `int_(0)^(1)(dx)/(x-sinx),`
(f) `int_(0)^(2)(1n(root4(x)+1))/(e^(tanx)-1)dx`

Answer

(a) It converges;
(b) diverges;
(c ) converges;
(d) converges;
(e ) diverges;
(f) converges.