## anonymous 3 years ago simple integration by substitution: 6-5sin(2x)

1. anonymous

|dw:1358068473382:dw|

2. anonymous

this is how far i got

3. AravindG

t=sin x would do it

4. AravindG

because derivative of sinx (ie cos x ) is readily available!

5. anonymous

you don't even need to use that trig identity by the way.

6. anonymous

just let $$u=2x$$ in the original integral, it'd work fine.

7. klimenkov

$$\int (6-5\cdot2\sin x \cos x)dx=\int6dx-10\int\sin x \cos xdx$$. Try to make a substitution $$t=\sin x,\quad dt=\cos x$$. Good luck.

8. AravindG

@wio'smethod is the simplest :)

9. anonymous

$\int \sin(2x)dx = \int \sin(u)\frac{ du}{2}$