`int(a^(x)dx)/sqrt(1-a^(2x))`

Evaluate: (i) int(a^x)/(sqrt(1-a^(2x)))\ dx (ii) int(2x)/(sqrt(1-x^2-x^4))\ dx

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

Let I_(1)=int_(1)^(2)(x)/(sqrt(1+x^(2)))dx and I_(2)=int_(1)^(2)(1)/(x)dx .Then

Evaluate: int(dx)/((x+1)sqrt(1+x-x^(2))

(9) int_(0)^(1)(dx)/(x+sqrt(1-x^(2)))

If the value of the integral I=int_(0)^(1)(dx)/(x+sqrt(1-x^(2))) is equal to (pi)/(k) , then the value of k is equal to

Evaluate: (i) int(e^x)/(sqrt(4-e^(2x)))\ dx (ii) int(x^2)/(sqrt(1-x^6))\ dx

Evaluate: (i) int(e^x)/(sqrt(4-e^(2x)))\ dx (ii) int(x^2)/(sqrt(1-x^6))\ dx

Evaluate: (i) int(e^x)/(sqrt(4-e^(2x)))\ dx (ii) int(x^2)/(sqrt(1-x^6))\ dx

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is