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Test the following integrals for converg...

Test the following integrals for convergence :
(a) `int_(1)^(oo)(1n(x^(2)+1))/(x)dx,`
(b) `int_(1)^(oo)(tan.(1)/(x))/(1+xsqrt(x))dx,`
(c ) `int_(1)^(oo)(2+cosx)/(sqrt(x))dx,`
(d) `int_(2)^(oo)(3+"arc"sin.(1)/(x))/(1+xsqrt(x))dx,`
(e ) `int_(1)^(oo)("arc"tanx)/(x)dx`.

Text Solution

Verified by Experts

The correct Answer is:
(a) It diverges.
(b) converges;
(c ) diverges.
(d) converges;
(e ) diverges
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