Question

Integration of
sin 2x.cos 5x•dx​

Answer 1

Step-by-step explanation:

We have,

$\int \sin(2x) \cos(5x) dx$

$= \frac{1}{2} \int2 \sin(2x) \cos(5x) dx$

$= \frac{1}{2} \int( \sin(7x) - \sin(3x) )dx$

$= \frac{1}{2} \int \sin(7x) dx - \frac{1}{2} \int \sin(3x) dx$

$= \frac{1}{2} \times (- \frac{ \cos(7x) }{7} ) - \frac{1}{2} \times ( - \frac{ \cos(3x) }{3} ) + c$

$= - \frac{ \cos(7x) }{14} + \frac{ \cos(3x) }{6} + c$