Question

Find the integral of x(2x+5)^8dx

Answer 1

@satellite73

Answer 2

@ganeshie8

Answer 3

\(\int x(2x+5)^8 dx\)

Put, 2x + 5 = u

Answer 4

What will be x and dx in terms of u ?

Answer 5

Du=2dx

Answer 6

I don't know if that's right though because you need to get back to xdx

Answer 7

you can use \[u=2x+5\]then solve the equation for \(x\) in terms of \(yu\)

Answer 8

i meant solve for \(x\) in terms of \(u\)

Answer 9

du = 2dx is correct

What about x in terms of u ?

Answer 10

But wouldn't that be du=2dx is there something I could do different?

Answer 11

Okay

Answer 12

it is kind of going to suck, but you can do it

Answer 13

Yeps :P

Answer 14

\[x=\frac{u-5}{2}\]

Answer 15

I've never done a problem like this

Answer 16

maybe it is a typo

Answer 17

It's out of a calculus book

Answer 18

No problem then.. Your integral will become:

\cfrac{1}{2}\[\int \cfrac{u - 5}{2}u^5 du\]

Answer 19

ok then grind it till you find it
btw calc books have typos too
lots of them

Answer 20

Why u^5? Hmmmm

Answer 21

Sorry the integral is:
\[\cfrac{1}{2}\int \cfrac{u - 5}{2}u^8 du\]

\[=\cfrac{1}{4} \int (u^9 - 5u^8) du\]

Answer 22

Can you solve this?

Answer 23

Yeah just a second I'm processing the information you just gave

Answer 24

Sure

Answer 25

The one thing I don't understand us why 1/2 is in front of the integral?

Answer 26

Recall that we got du = 2dx
=> dx = du/2

So, this is where we got that that 1/2

Answer 27

Oh okay!

Answer 28

I got 1/40(2x+5)^10-5/36(2x+5)^9

Answer 29

Sorry if that's hard to read

Answer 30

Perfect!! Don't forget the integration constant C

Answer 31

I always forget it!!!! Ugh!!!!

Answer 32

:) It's alright!

Answer 33

Thank you so much :)

Answer 34

Glad to be of help :)

Answer 35

Definitely a fan

Answer 36

Would you be able to help with a different topic soon?

Answer 37

I'm not good at intragration by parts