Question

integration (2 + sin 2x) dx​

Answer 1

Question:

• $\displaystyle\int (2+\sin x )dx$

Solution:

$\longmapsto\displaystyle\int (2+\sin x )dx\\\\\implies\displaystyle\int 2\;dx+\int\sin x \; dx \\\\\\\red\bigstar\boxed{\int 2\;dx=2}\\\\\\\implies 2x -\cos x \\\\\star\bf Add \; constant\;to\;the\;solution\\\\\implies\sf \pink{ 2x -\cos x+c}$

More to know :

• ∫ sin x dx = -cos x + c
• ∫ cos x dx = sin x + c

Answer 2

Answer:

Taking the 2 out of the integration.

That will give u 2|sin2x dx= 2(-cos2x)/2

=-2cos2x/2+C = -cos2x+C

(| =Integration sign)