Is equal to, where is constant of…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

\int \frac{\cos x\,dx}{\sqrt{\sin^2 x + 2\cos^2 x}}

is equal to, where

C

is constant of integration. (a)

\sin^{-1}\left(\frac{\sin x}{\sqrt{2}}\right) + C

(b)

\ln(\sin x + \sqrt{2 - \sin^2 x}) + C

(c)

\sin^{-1}\left(\frac{\sin x}{2}\right) + C

(d)

\ln(\sin x - \sqrt{2 - \sin^2 x}) + C