Question

The integral of Sin2x/Sinxdx

Answer 1

Sin(2x) is a trig identity which expands out to 2sinxcosx.

Answer 2

Okay then should I set u=sin2x? and dv=dx

Answer 3

No. if sin2x = 2sinxcosx, you can cancel out the sinx

Answer 4

Okay so I set u=2sinxcosx?

Answer 5

There is no u substitution.

sin2x is a trig identity

sin2x is EQUAL to 2sinxcosx.

This means that your equation can be rewritten as 2sinxcosx/sinx.

You can cancel out the sinx

So you end up with 2cosx

And then take the integral of 2cosxdx

Answer 6

Okay....Then u should be cosxdx?

Answer 7

Where is u coming from?

Answer 8

From the last part integral of 2cosxdx

Answer 9

When I take the integral of that should u=cosx?

Answer 10

Where is u?

The integral is just
\[\int\limits_{}^{}2cosxdx\]

Answer 11

I need to find the anti-derivative to the integral of 2cosxdx

Answer 12

Yes.

Answer 13

So shouldnt I set u=cosx

Answer 14

\[1/2\int\limits_,2cosxdx\] u=cosx, du=sinxdx

Answer 15

You don't need u at all.
\[\int\limits_{}^{}2cosxdx = 2\int\limits_{}^{}cosxdx\]

Which equals 2sinx + c.