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" 4."int(0)^(oo)(dx)/(x^(2)sqrt(a^(2)+x^...

" 4."int_(0)^(oo)(dx)/(x^(2)sqrt(a^(2)+x^(2)))

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Prove that int_(a)^(oo) (dx)/(x^(4)sqrt(a^(2) + x^(2)))=(2-sqrt(2))/(3a^(4))

int_(0)^(oo)(dx)/([x+sqrt(1+x^(2))]^(n)

int_(0)^(2)(dx)/(x+sqrt(4-x^(2)))

int_(0)^(oo)(dx)/((1+x^(2))^(4))=

int_(0)^(oo)(dx)/((x+sqrt(x^(2)+1))^(3))=

int_(0)^(oo) (ln x)/(x^(2)+a^(2))dx=

int_(0)^(oo) (dx)/((x+sqrt(x^(2)+1))^(3))=

I=int_(0)^(oo)(x)/((x^(2)+a^(2))^(2))dx

int_(0)^(oo) (dx)/((1+x^(2))^(4))=

int_(0)^(oo) (dx)/([x+sqrt(x^(2)+1)]^(3))dx=