[(x)/(9-4x^(2))],[e^(tan^(-1)x)]

If 2sin^(-1)((9-4x^(2))/(9+4x^(2)))+3cos^(-1)((12x)/(9+4x^(2)))+tan^(-1)((12x)/(9-4x^(2)))=lambda(pi)/(2) for x=(-17)/(13) "then" lambda

If 2sin^(-1)((9-4x^(2))/(9+4x^(2)))+3cos^(-1)((12x)/(9+4x^(2)))+tan^(-1)((12x)/(9-4x^(2)))=(lambda pi)/(2) for x=(-17)/(13) then lambda

Integrate the functions (1)*(x)/(9-4x^(2)) (2) *e^(2x+3)

If y = tan ^(-1) ((2x )/( 1 -x ^(2))) + tan ^(-1) ((3x - x ^(3))/( 1 - 3x ^(2)))- tan ^(-1) ((4x - 4x ^(3))/( 1 - 6x + x ^(4))), then show that (dy)/(dx) = (1)/(1 + x ^(2)).

Prove that : 1/6tan^(-1)""(2x)/(1-x^2)+1/9tan^(-1)""(3x-x^2)/(1-3x^2)+1/12 tan^(-1)""(4x-4x^3)/((1-6x^2+x^4))= tan^(-1)x

If alpha=int_0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)x takes only principal values, then, find the value of ((log)_e|1+alpha|-(3pi)/4)

If alpha=int_(0)^(1)(e^(9x+3tan^(-1)x)((12+9x^(2))/(1+x^(2)))dx where tan^(-1)x takes only principal values, then the value of (log_(e)|1+alpha|-(3pi)/(4)) is-

Show that int_(0)^(1)(e^(x))/(1+e^(2x))dx=tan^(-1)(e)-pi/(4)

int e^(tan^(-1)x)(1+x+x^(2))d(cot^(-1)x) is equal to -e^(tan^(-1)x)+c(b)e^(tan^(-1)x)+c-xe^(tan^(-1)x)+c(d)xe^(tan-1)x+c