[" Fिमनलित्ति बा "x" ढि सा' "],[" 1.(i) "(x)/(1+x^(2))]

If I_(1) int sin^(-1) ((2x)/(1 +x^(2)) ) dx , I_(2) = int cos^(-1) ((1-x^(2))/(1 +x^(2)) ) dx , I_(3) = int tan^(-1) ((2x)/(1 - x^(2)) ) dx , then I_(1) + I_(2) - I_(3) =

If x=2sqrt(3)+2sqrt(2) , find : (i) 1/x" (ii) "x+1/x" (iii) "(x+1/x)^(2)

I=int(1-x^(2))/(x(1-2x))dx

Integrate the following with respect to 'x' : (i) (1+x^2)^(-1) (ii) (1-x^2)^(1/2)

I=int(1)/(x^(3)+x^(2)+x+1)dx

If i= sqrt(-1) , prove that following (x+1+ i) (x + 1- i) (x-1 + i) (x-1-i)= x^(4) + 4

If i= (sqrt-1) , prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)= x^(4) + 4

Solve for x (i) 2^(|x+1|)+2^(|x|)=6 and x in I (ii) x^(2)+x+1+|x-3| le |x^(2)+2x-2| (iii) |2x-4|-2|x^(2)+x-3|+2|x-1||x+1|=0

Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions. Then which of the following does not hold good? a. z=1/(1-i x)+i1/(1+i x) b. z=1/(1+i x)+i1/(1-i x) c. z=1/(1+i x)+i1/(1+i x) d. z=1/(1-i x)+i1/(1-i x)

Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions. Then which of the following does not hold good? a. z=1/(1-i x)+i1/(1+i x) b. z=1/(1+i x)+i1/(1-i x) c. z=1/(1+i x)+i1/(1+i x) d. z=1/(1-i x)+i1/(1-i x)