Finding the Indefinite Integral: Can Multiplying a Constant Change the Solution?

[Scholar1]

I have posted my attempt and the problem above. Please help!

Thanks in advance!

 

[SteamKing]

I have posted my attempt and the problem above. Please help!

Thanks in advance!

It's hard to mark up an image.

The factor of (1/2) multiplies not only ∫ 1 dx but also ∫ -cos 6x dx, which you omitted from the second integral.

After you have found the correct integrals, you can use the double angle formulas to convert these from trig functions in 6x to trig functions in 3x.

 

[Scholar1]

So if I put - (1/12) in front of the sin6x it would be correct?

 

[SteamKing]

So if I put - (1/12) in front of the sin6x it would be correct?

Yesss...multiplication distributes over addition and subtraction.