If `(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))=K ((a^(2))/(x^(2)+a^(2))-(b^(2))/(x^(2)+b^(2)))` then K=

int(x)/((x^(2)-a^(2))(x^(2)-b^(2)))dx

(x^(2)+5)/((x^(2)+2)^(2))=(1)/(x^(2)+2)+(k)/((x^(2)+2)^(2))

int_(0)^(oo)(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))dx=(pi)/(2(a+b))

If the locus of the middle point of the portion of a tangent of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 included between the axes is ((a^(2))/(x^(2)))+((b^(2))/(y^(2)))=k, then the value of k is

int(2x^(2)+a^(2))/(x^(2)(x^(2)+a^(2)))dx=(k)/(x)+(1)/(a)Tan^(-1)((x)/(a))+c then k

Simplify :((x^(a))/(x^(b)))^(a^(2)+b^(2)+ab)xx((x^(b))/(x^(c)))^(b^(2)+c^(2)+bc)xx((x^(c))/(x^(a)))^(c^(2)+a^(2))

((x^(a))/(x^(-b)))^(a^(2)-ab+b^(2))times((x^(b))/(x^(-c)))^(b^(2)-bc+c^(2))times((x^(c))/(x^(-a)))^(c^(2)-ca+a^(2))