`intxdx/((1-x^(2))`

int((1-x^(-2))/(x^(1/2)-x^(-1/2))-(2)/(x^(3/2))+(x^(-2)-x)/(x^(1/2)-x^(-1/2)))dx

If (ax-1)/((1-x+x^(2))(2+x))=(x)/(1-x+x^(2))-(1)/(2+x) then, a=

simplify 2tan^(-1)((1+x)/(1-x))+sin^(-1)((1-x^(2))/(1+x^(2)))

If x_(1) = 2 tan^(-1) ((1 + x)/(1 -x)), x_(2) = sin^(-1) ((1 - x^(2))/(1 + x^(2))), " where " x in (0, 1) , then x_(1) + x_(2) is equal to

To prove that tan((1)/(2)sin^(-1)((2x)/(1+x^(2)))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2)))=(2x)/(1-x^(2))

sin{tan^(-1)[(1-x^(2))/(2x)]+cos^(-1)[(1-x^(2))/(1+x^(2))]}=

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

Solve 3sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+2tan^(-1)((2x)/(1-x^(2)))=(pi)/(3)

If x+(1)/(x)=3, then find x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))