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**AlexPA****Guest**

Hi,

How do i work out the integral of the following 2: I dont know how to deal with the constants (C and B)

y = C cos (4x)

y = tan (-Bx)

Thanks alot, Alex

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

The first one is fairly simple.

C is just a constant so we can remove that and put it back in at the end.

We know that d(sin(4x))/dx = 4cos 4x, so naturally that means that 4cos 4x integrates to give sin (4x).

However, we want to integrate cos 4x. This is 4 times smaller than 4cos 4x, so we divide the result of that integral by 4.

∫ cos xdx = C/4 sin 4x + c.

c is an arbitrary constant that must always be included when integrating.

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The second one is harder, because the integral of tan x is less well known. Searching on the internet shows that it is ln |sec x| + c. Now we know this, we can use the same reasoning as in the above example to show that the integral is -1/B * ln|sec x| + c.

Why did the vector cross the road?

It wanted to be normal.

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