Question

integral of cos6x dx
plz help!!

Answer 1

\[\frac{ \sin(6x) }{ 6 } + C\]
because its derivative is cos(6x)

Answer 2

:O

Answer 3

how did u get that?? @Euler271

Answer 4

???? @zepdrix

Answer 5

what's the derivative of cos(6x)?

Answer 6

-sin6x ???? @Euler271

Answer 7

-6sin6x

Answer 8

the integral is the inverse operation of the derivative.

so the integral of -6sin6x must be cos6x.

tbh i dont even know how to explain it lol. i hope this helps

Answer 9

yea sorry!! I get u! thanks!@Euler271

Answer 10

^_^

Answer 11

That's a good method to get comfortable with, just sort of like.. advanced guessing.
You know that the derivative will produce an extra factor of 6 because of the 6x inside of the trig function.

So when we integrate, we need to divide by a factor of 6.

If this is still confusing though, you can certainly perform a u-substitution:\[\Large \int\limits \cos6x\;dx,\qquad\qquad u=6x\]