`int_-1^3 [tan^-1 frac{x}{x^2+1)+cot^-1 frac{x}{x^2+1}]dx`

If abs(x) lt 1 , the prove that 2tan^-1x = tan^-1(frac{2x}{1-x^2}) = sin^-1(frac{2x}{1+x^2}) = cos^-1(frac{1-x^2}{1+x^2})

Differentiate the following w.r.t. x: tan^(-1)[frac{x}{1+6x^2}] + cot^(-1)[frac{1-10x^2}{7x}]

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

Evaluate: \int_{0}^1 frac{1}{1+x^2} sin^(-1)(frac{2x}{1+x^2}) dx

If tan^-1(frac{x-1}{x-2})+tan^-1(frac{x+1}{x+2}) = frac{pi}{4} then find value of x

Show that tan^-1(frac{3a^2x-x^3}{a^3-3ax^2})=3tan^-1frac{x}{a}

Show that tan^-1frac{x}{sqrt(a^2-x^2)}=sin^-1frac{x}{a}

Solve for x: tan^-1 (frac{x}{2}) + tan^-1(frac{x}{3}) = frac{pi}{4}, x > 0

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

Show that cot^-1(frac{1}{3})-tan^-1(frac{1}{3}) = cot^-1(frac{3}{4})