$\int \frac{sin x + 4 sin 3 x + 6 sin 5 x + 3 sin 7 x}{sin 2 x + 3 sin 4 x + 3 sin 6 x} d x$ equals.

- 2 sin x + c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 sin x + c

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 cos x + c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 2 cos x + c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2 sin x + c$
$\int (\frac{s i n x + 4 sin 3 x + 6 sin 5 x + 3 sin 7 x}{sin 2 x + 3 sin 4 x + 3 sin 6 x} d x)$
To evaluate the integral
Sol.:
$s i n x + sin 3 x + 3 s i n x + (3 sin 5 x + 3 sin 5 x) + 3 sin 7 x$
= $(s i n x + sin 3 x) + 3 (sin 3 x + sin 5 x) + 3 (sin 5 x + sin 7 x)$
$= 2 sin 2 x c o s x + 3 (2 sin 4 x c o s x) + 3 (2 sin 6 x c o s x)$
$∴ I = \int (2 c o s x (\frac{(sin 2 x + 3 sin 4 x + 3 sin 6 x)}{(sin 2 x + 3 sin 4 x + 3 sin 6 x)}) d x$
$= \int (2 c o s x d x) = 2 s i n x + C$
Hence, correct answer is $2 sin x + C .$

Suggest Corrections

Similar questions

\int \frac{s i n x + 4 s i n 3 x + 6 s i n 5 x + 3 s i n 7 x}{s i n 2 x + 3 s i n 4 x + 3 s i n 6 x} d x

\int \frac{3 + 2 c o s x}{(2 + 3 c o s x)^{2}} d x

\int \frac{d x}{s i n x + s i n 2 x} =

\int \frac{\cos \sqrt{x}}{\sqrt{x}} d x

\sqrt{x}

\sqrt{\frac{\cos x}{x}} + C

\sqrt{x} + C

\sqrt{x} + C

\int \frac{sin \frac{5 x}{2}}{sin \frac{x}{2}} d x

c

Join BYJU'S Learning Program