If you used Clearing in 2024, how did you find it?

Integration

Aired

How do you integrate (9x)/(3x-8)dx ?

It's probably really simple but I can't see which method to use.

Reply 1

dvs

(9x)/(3x-8) = 3 (3x)/(3x-8) = 3 (3x-8+8)/(3x-8) = 3 (1 + 8/(3x-8)) = 3 + 24/(3x-8)

Reply 2

Aired

dvs

(9x)/(3x-8) = 3 (3x)/(3x-8) = 3 (3x-8+8)/(3x-8) = 3 (1 + 8/(3x-8)) = 3 + 24/(3x-8)

I don't understand what you've done there :confused:

Reply 3

dvs

(3x-8+8)/(3x-8) = (3x-8)/(3x-8) + 8/(3x-8)

It's a very common 'trick' to add zero to things.

Reply 4

Aired

Ohhh, ok thanks alot!

Reply 5

dvs

You're welcome. :smile:

As a side note, you could have used long division.

Reply 6

Simba

Aired

How do you integrate (9x)/(3x-8)dx ?

It's probably really simple but I can't see which method to use.

Alternatively use the substitution u = 3x - 8.

du/dx = 3

du = 3dx

x = (u + 8)/3

=> INT[9x/(3x - 8)]dx = INT[3x/u]du

= INT[(u + 8)/u]du

= INT[1 + 8/u]

= u + 8ln|u|

= 3x - 8 + 8ln|3x - 8|

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