Question

integral of (2x+1)(x^2+x)^9 dx, using u=x^2+x

Answer 1

If u = x^2 + x, then du = (2x+1) dx

So the integral is of the form, u^9 du

and the integral of u^9 du is just u^10/10

So substitute u = 2x + 1 for u, so your final answer is (2x+1)610/10 + c

Dont forget the + C at the end.

Answer 2

is that a 610 or ^10?

Answer 3

ir recon it is, thanks mate i got it!!!

Answer 4

Sorry, thats(2x+1)^10

Answer 5

typo error

Answer 6

awesome, do you mind if i ask another one that has got sim and cos in ti???

Answer 7

***sin and cos in it???

Answer 8

yes

Answer 9

go ahead

Answer 10

integral of (sinx)/(cos^4x)dx, using u = cos x

Answer 11

let u= cos (x); so du = - sin x dx

So what form does this integral take? Thats the crucial question, the form that the integral takes.

Well......

Answer 12

it just tells me to solve the integral but i have to use that specific substitution to do it

Answer 13

We pull the minus sign in front of the integral, and it takes the form of u^4 du Agree?????????

Answer 14

Let me ne very specific...the integral is (sin x) (cos^4x) ds....so the sin x dx...thats just -du (because du = - sin x)

Answer 15

So the inegrand (whats inside the integral sin) is of the form u^4 du

Answer 16

agree?

Answer 17

i agree that its -du

Answer 18

If u = cos x and du = - sin x dx

By substitution, isnt (sin x)(cos^4x) dx = - u^5 du??????

Answer 19

sorry, I meant u^4 du

Answer 20

and just be clear only the 4 is ^ in the cos part not the x
does that make sense to you

Answer 21

u = cos x , so cos^4x is just u^4

Answer 22

correct..only the 4 is in the exponent

Answer 23

cool thats the part that was messing with my head lol

Answer 24

so the integral is of the form of u^4 du with a minus sign on the outside of the integral

Answer 25

The integral of u^4 du is just u^5/5 + C...agree???????

Answer 26

yep that sounds right and then all i have to do is substitute cos x back in right?

Answer 27

exactly...final answer is - (cos x)^5/5 + C

Dont forget that minus sign in the front as we pulled out the minus sign

Answer 28

ohh right. thanks mate your a real life legend. it was stumping me for ages

Answer 29

Review this problem..I dont want it to sound right..I want to make sure that you are crystal clear about this problem!

Answer 30

alright hang on an ill read through it. i sec

Answer 31

It's not a novel for reading..It must be gone through very carefully with a solid understanding!

Answer 32

yep, i get it thats heaps great. the 4 in between the cos and x was getting to me but i understand now, thanks heaps