" (e) "f(x)(x+1)^(3)(x-3)^(3)

(1)/(e^(3x)+e^(-3x))

Evaluate int(x-3)/((x-1)^(3))e^(x)dx . Here, the integrand (x-3)/((x-1)^(3)) is not in the form of e^(x)[f(x)+f'(x)] , so we firstly convert it in the form of e^(x)[f(x)+f'(x)] and then simplify it

If f(x) is polynomial function such that f(x)+f'(x)+f(x)+f'(x)=x^(3) and g(x)=int(f(x))/(x^(3)) and g(1)=1 then g( e ) is

The function f : (-oo, 3] to (o,e ^(7)] defined by f (x)=e ^(x^(3)-3x^(2) -9x+2) is

The function f : (-oo, 3] to (o,e ^(7)] defined by f (x)=e ^(x^(3)-3x^(2) -9x+2) is

If f(x)=log((1+x)/(1-x))a n dg(x)=((3x+x^3)/(1+3x^2)) , then f(g(x)) is equal to (a) f(3x) (b) {f(x)}^3 (c) 3f(x) (d) -f(x)

Find the inverse of the following function.( i ) f(x)=sin^(-1)((x)/(3)),x in[-3,3]( ii )f(x)=5^(log_(e)x),x>0 (iii) f(x)=log_(e)(x+sqrt(x^(2)+1))

If f(x)=x+(1)/(x) , then prove that : {f(x)}^(3)=f(x^(3))+3*f((1)/(x))