Question

Find the integral of (lnx^3)/x? Confused..

Answer 1

substitute \(u = \ln x \)

Answer 2

before that, simplify the log

Answer 3

use below property :

\(\ln a^b = b\ln a\)

Answer 4

ohhh okay that was what was making me stuck; the u! By the way.. if you're taking an integral of something and it's a product of two quantities, how do you take the integral?

Answer 5

there is no standard way for taking integral of product/quotient of two functions

Answer 6

as opposed to the derivative being able to use the chain rule?

Answer 7

oops sorry, product rule*

Answer 8

and u wont be successful most of the time

Answer 9

yes, there is not standard way for product of functions

Answer 10

we can take "derivative " of any complicated evil funciton manually.

Answer 11

but we cannot take "integral" of everything manually

Answer 12

and there are no product/quotient rules for integrals.

Answer 13

got it :) thanks so much!

Answer 14

np :)