Question

$\int_{}^{}{x^{51}(\tan^{- 1}x + \cot^{- 1}x)\mspace{6mu} dx =}$

• A. $\frac{x^{52}}{52}(\tan^{- 1}x + \cot^{- 1}x) + c$
• B. $\frac{x^{52}}{52}(\tan^{- 1}x - \cot^{- 1}x) + c$
• C. $\frac{\pi x^{52}}{104} + \frac{\pi}{2} + c$
• D. None of these

Answer 1

Answer: (C)

$\frac{\pi x^{52}}{104} + \frac{\pi}{2} + c$

Answer 2

$\int_{}^{}{\frac{\cos 2x}{(\cos x + \sin x)^{2}}\mspace{6mu} dx =}$

$\log\sqrt{\cos x + \sin x} + c$.