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int(0)^(a)(x^(4))/(sqrt(a^(2)-x^(2)))dx...

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

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int_(0)^(a) (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)

The value of int_(0)^(a)(dx)/(x+sqrt((a^(2)-x^(2))) is equal to

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