Pure Maths integration and Vectors

[superduper2009]

I'm talking about paper 1 i.e. pure maths in CIE maths
Guys I cant figure out the following... i really need help in integration when it involves brackets...

can you tell me a general formula for integrating a function...
lets say
y= a(bx+c)^n

where a, b, c are constants....
can you please tell me what the integrated term would be...
and the steps involved in getting the integrated terms...

Regarding vectors...
What are the steps of finding unit vector... for e.g. in O/N 2004, paper 1 CIE, q 8
thanks in advance

[astarmathsandphysics]

(a/(b(n+1))(bx+c)^(n+1)

[Baladya]

For the vectors its really easy... Imagine this as a normal calculation. Order of operation tells u to first do multiplication, so for: a – 2b. u do 2b (2xb) first. This is matrix, all u gotta do is multiply each number in the parenthesis by -2. It will be ( 2  )
                                                                                                                                                                                                        ( -4)
now u have to do the addition/subtraction.  (3+2)       ( 5 )
                                                                                (4-4)=     ( 0  )

[astarmathsandphysics]

If z=(x,y) unit vector is (x,y)/sqrt(x^2+y^2)

[superduper2009]

astar ....man ur da best....thanks sooooo much

just one more question...
 what if the x term inside the bracket has a power...
so in this case what do we do

y= a(bx^z+c)^n

+rep

[cashem'up]

astar ....man ur da best....thanks sooooo much

just one more question...
 what if the x term inside the bracket has a power...
so in this case what do we do

y= a(bx^z+c)^n

+rep

yea that used to bug me a lot.......but then when u differentiate such u use the chain rule.....so then i dont noe i was playin aroun and i think u use some reverse kinda chain rule......but then that was me playin even though the answers were comin... no guarantee waait for astar to tell us........

[astarmathsandphysics]

expand the brackets and integrate term by term

[cashem'up]

expand the brackets and integrate term by term

but what would  u do if the powers are very high..............

[astarmathsandphysics]

try the substitution x=sqrt(c/b) tanu