If `(frac{a}{b})^(x-1)=(frac{b}{a})^(x-3)`, then the value of x is:

If int frac{xdx}{x^2-4x+8}=K log (x^2-4x+8)+tan^(-1)(frac{x-2}{2})+C , then the value of K is:

If f(x)=x^3-frac{1}{x^(3)} find the value of f(x)+f(frac{1}{x})

int frac {dx}{x(x^4+1)

If lim_(x->0)(1+a x+b x^2)^(2/x)=e^3, then find the value of a and b.

If lim_(x to 0) (x(1 + a cos x)-b sinx)/(x^3) = 1 , then the value of ab is euqal to

If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is (a) 0 (b) 2 (c) 1 (d) 3

Let cos^(-1) (4x^(3) -3x) = a + b cos^(-1) x If x in [-1, -(1)/(2)) , then the value of a + b pi is

If the largest interval of x in which the function f(x)=x^(3)-3x+1 is decreasing is (a, b), then the value of a+2b is equal to

int frac{x}{x^2sqrt(x^4-1)} dx

3frac{1}{13}+1frac{4}{13}+2frac{3}{13}