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int2x sqrt(x)dx" on "(0,oo)...

int2x sqrt(x)dx" on "(0,oo)

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(i) int_0^a sqrtx/(sqrtx+sqrt(a-x)) dx (ii) int_0^5 sqrtx/(sqrtx+sqrt(5-x)) dx (iii) int_0^a (dx)/(x+sqrt(a^2+x^2))

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta