Question #526f5

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Answer 1 · 2016-06-20T14:15:04

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

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

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