" 21."int(0)^((pi)/(x+sqrt(a^(2)-x^(2)))...

" 21."int_(0)^((pi)/(x+sqrt(a^(2)-x^(2))))dx

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

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

int_(0)^((pi)/(4))sqrt(1+sin2x)dx

The value of the expression (int_(0)^(a)x^(4)sqrt(a^(2)-x^(2))dx)/(int_(0)^(a)x^(2)sqrt(a^(2)-x^(2))dx)=

int_(0)^(pi) sqrt((1+cos 2x)/(2))dx=

int_(0)^( pi)(sqrt(1+cos2x))/(2)dx

int_(0)^((pi)/(4)) sqrt(1+sin 2x) dx =

int_(0)^(pi//4)sqrt(1+cos2x)dx

int_(0)^(1)x.sqrt((1-x^(2))/(1+x^(2)))dx=(pi-2)/(4)

int_(0)^(pi//2)(1)/(1+sqrt(tan x))dx=

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