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int(0)^(1)(sin^(-1)sqrt(x))/(x^(2)-x+1)d...

int_(0)^(1)(sin^(-1)sqrt(x))/(x^(2)-x+1)dx" is "(pi^(2))/(sqrt(n))(n

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If the value of the definite integral int_(0)^(1)(sin^(-1)sqrt(x))/(x^(2)-x+1)dx is (pi^(2))/(sqrt(n)) (where n in N), then the value of (n)/(27) is

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int_(0)^((pi)/(4))sin^(-1)sqrt((x)/(a+x))dx

int_(0)^((pi)/(4))sin^(-1)sqrt((x)/(a+x))dx

Show that int_(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt(3))/(12)pi

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

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

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