#1**+10 **

**I think it must be sin4(x-3) insted of cos4(x-3) in the last step !**

**Yes!**

Because: $$\int{\cos(4u)}\ du = \frac{1}{4}\sin(4u)$$

.heureka Feb 13, 2015

#2**0 **

Also in this question, why they didn't wrote $$\frac{1}{2}(x+1)$$ insted of $$\frac{1}{2}x$$ !

xvxvxv Feb 13, 2015

#3**+10 **

$$\frac{1}{2}\int (1+\cos{2(x+1)})dx=\frac{1}{2}\int dx+\frac{1}{2}\int \cos{2(x+1)}dx$$

so the single x comes from the first integral on the right-hand side. However, you could add whatever constant you like, because, as it's an indefinite integral, any other constants are accounted for in the "c" at the end.

.

Alan Feb 13, 2015