Question

Question #526f5

Answer 1

`\int sin(2x)dx = -cos(2x)/2+C`

Explanation:

We know that the integral of `sin(x)` is `-cos(x)`.
In this case the only difference is that it is `2x` instead of `x`.

We can substitute the variable

`2x=y` and we need to substitute also the differential

`x=y/2` so `dx=dy/2`.

We are ready for our integral

`\int sin(2x)dx=\int sin(y)/2dy=-cos(y)/2+C`

and substituting back

`-cos(y)/2+C=-cos(2x)/2+C`.