help with logarithmic integration. I've been googling some tutorials on integrating logarithms for my calc 2 class and I've found a lot of good stuff. Unfortunately nothing has answered how to handle a problem that I have. I've tried u-substitution and have still been getting it wrong or just lost. My problem is the int((9)/(x^3) + (2)/(9x))dx (sorry, I'm a little new to the math section and don't know how to format that nicely). So far I've tried finding a common denominator which changes the equation to (81+2x^2)/(9x^3). I tried doing u=9x^3 and du=27x^2dx or 1/(27)du=x^2 dx. Now the problem is kind of ugly and I'm not sure what to do with that next. We haven't covered integration by parts yet in this class and I've found that comes up, so I'm not sure if it's possible to evaluate witho

musicbachv7

musicbachv7

Answered question

2022-08-11

help with logarithmic integration.
I've been googling some tutorials on integrating logarithms for my calc 2 class and I've found a lot of good stuff. Unfortunately nothing has answered how to handle a problem that I have. I've tried u-substitution and have still been getting it wrong or just lost. My problem is the ( 9 x 3 + 2 9 x ) d x (sorry, I'm a little new to the math section and don't know how to format that nicely). So far I've tried finding a common denominator which changes the equation to 81 + 2 x 2 9 x 3 . I tried doing u = 9 x 3 and d u = 27 x 2 d x or 1 27 d u = x 2 d x. Now the problem is kind of ugly and I'm not sure what to do with that next. We haven't covered integration by parts yet in this class and I've found that comes up, so I'm not sure if it's possible to evaluate without that technique. I really appreciate any help!
Thank you in advance

Answer & Explanation

Payton Mcbride

Payton Mcbride

Beginner2022-08-12Added 18 answers

There is no need to use substitution in this case. This is pretty straight forward and can be calculated directly using the formula.
( 9 x 3 + 2 9 x ) d x
= 9 x 3 d x + 2 9 d x x
= 9 ( x 3 + 1 3 + 1 ) + 2 9 ln x + c
= 9 2 1 x 2 + 2 9 ln x + c
= 9 2 1 x 2 + 2 9 ln x + c
x n d x = x n + 1 n + 1 + c , 1 n Z
d x x = ln x + c. This is a special case of the previous formula for n = 1

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