(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))=k[(...

(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))=k[(a^(2))/(x^(2)+a^(2))-(b^(2))/(x^(2)+b^(2))]rArr k=

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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=

intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e r ea , b in R^+)i se q u a lto 1/(6lna^2b^3)a^(2x)b^(3x)ln(a^(2x)b^(3x))/e+k 1/(6lna^2b^3)1/(a^(2x)b^(3x))ln1/(e a^(2x)b^(3x))+k 1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k -1/(6lna^2b^3)1/(a^(2x)b^(3x))ln(a^(2x)b^(3x))+k

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=0

If f(x)sin x cos xdx=(1)/(2(b^(2)-a^(2)))ln f(x)+c, then f(x) is equal to (1)/(a^(2)sin^(2)x+b^(2)cos^(2)x)(b)(1)/(a^(2)sin^(2)x-b^(2)cos^(2)x+b^(2)cos^(2)x+b^(2)cos^(2)x)(d)(1)/(a^(2)cos^(2)x-b^(2)cos^(2)x)

If (x^(2)+5)/(x^(2)+2)^(2)=1/(x^(2)+2)+k/(x^(2)+2)^(2) " then " k=

(x^(2))/((x^(2)+a^(2))(x^(2)+b^(2)))=k[(a^(2))/(x^(2)+a^(2))-(b^(2))/(x^(2)+b^(2))]rArr k=

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