`int_(0)^1 1/sqrt(x) dx`

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int_0^1 1/sqrt(5x+3) dx=

int_0^1 x/sqrt(1+x)dx

int_(0)^(1)sqrt(x)dx=

int_(0)^(1)sqrt(x+1) dx =

int_(0)^(1)x sqrt(1-x)dx

int_0^1 x/(1+sqrt(x))dx

int_0^1 x/sqrt(1+x^2)dx

int_0^1 x/sqrt(1-x^2)dx

int_(0)^(1)x+sqrt(x)dx=

[-int_(0)^(1)sqrt(1-x)dx],[=(pi)/(2)-1]