$\int sin x \sqrt{1 + cos 2 x} d x$

Open in App

Solution

$\int s i n x \sqrt{1 + c o s 2 x} d x = \int s i n x \sqrt{1 + 2 c o s^{2} x - 1} d x = \sqrt{2} \int s i n x c o s x d x = (\frac{\sqrt{2}}{2}) \int 2 s i n x c o s x d x = (\frac{1}{\sqrt{2}}) \int s i n 2 x d x = (\frac{1}{\sqrt{2}}) \cdot (\frac{- c o s 2 x}{2}) + C = (\frac{- c o s 2 x}{2 \sqrt{2}}) + C$

Suggest Corrections

Similar questions

\int \frac{sin x}{1 + {cos}^{2} x} d x

\int sin x \sqrt{1 - cos 2 x} d x

\int sin x \sqrt{1 + cos 2 x} d x

\int e^{x} (\frac{cos x - sin x}{1 - cos 2 x}) d x =

\int \frac{1 - sin x}{{cos}^{2} x} d x

Join BYJU'S Learning Program