U-substitution Problem: Solve ∫(3x-12)/(x2+4x+13) dx by substituting x=3t-2

[help meeeeeeee]

Hi im stuck on the last problem of a chapter in my book and it goes:

Solve ∫(3x-12)/(x²+4x+13) dx by substituting x=3t-2

Can someone help me solve it? thank you

 

[Deleted member 4993]

Hi im stuck on the last problem of a chapter in my book and it goes:

Solve ∫(3x-12)/(x²+4x+13) dx by substituting x=3t-2

Can someone help me solve it? thank you

The suggested substitution is then:

t = (x + 2)/3

Does that provide a clue to you?

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[help meeeeeeee]

Yes. I figured t=(x+2)/3 and dt=dx/3 but how do i substitute t into the equation and how many t are there?? I tried to make the equation easier but Partial fraction isnt possible on the denominator so i get nowhere

please help

 

[Deleted member 4993]

Hi im stuck on the last problem of a chapter in my book and it goes:

Solve ∫(3x-12)/(x²+4x+13) dx by substituting x=3t-2

Can someone help me solve it? thank you

(3x - 12)/(x^2+4x+3) = 3 * [(x + 2) - 6]/[(x +2)^2 + 3^2]

What do you get from above?

Simple algebra......

 

[help meeeeeeee]

ok then what? i get ∫-15/(x+11) and thats -15ln(x+11) but thats very wrong

anyways i solved it and the answer is 3/2ln(x^2+4x+13)-6arctan((x+2)/3)+C

so yeah not so simple algebra after all..

 

[Deleted member 4993]

ok then what? i get ∫-15/(x+11) and thats -15ln(x+11) but thats very wrong

anyways i solved it and the answer is 3/2ln(x^2+4x+13)-6arctan((x+2)/3)+C

so yeah not so simple algebra after all..

It is simple algebra when done correctly!

How are you getting 'x' in the denominator - after replacing 'x' with the given substitution??

(3x - 12)/(x^2+4x+3) dx = 3 * [(x + 2) - 6]/[(x +2)^2 + 3^2] dx

after substitution

3 * [ 3*t - 6]/[9*t^2 + 9] * 3 * dt

= 3 * (t - 2)/(t^2 + 1) dt

= 3/2 * [2t dt /(t^2 + 1) - 4 dt/(t^2 + 1)] integrating....... edited

= 3/2 * [ ln(t^2 + 1) - 4 arctan(t)] ....... edited

Now back substitute ....

Simple algebra after all ..... carefully done....

 

[help meeeeeeee]

when substituting back your answer 3/2 * [ ln(t^2 + 1) + 2 arctan(t + 1)] it doesnt equal to my answer 3/2ln(x^2+4x+13)-6arctan((x+2)/3)
so i guess we can agree it's not simple algebra

 

[Steven G]

when substituting back your answer 3/2 * [ ln(t^2 + 1) + 2 arctan(t + 1)] it doesnt equal to my answer 3/2ln(x^2+4x+13)-6arctan((x+2)/3)
so i guess we can agree it's not simple algebra

It is simple algebra. If you think otherwise then you need to state why it isn't, that is state where it is not simple.

 

[Steven G]

when substituting back your answer 3/2 * [ ln(t^2 + 1) + 2 arctan(t + 1)] it doesnt equal to my answer 3/2ln(x^2+4x+13)-6arctan((x+2)/3)
so i guess we can agree it's not simple algebra

It was left for YOU to figure out that it is -4 arctan(t) and not + 2 arctan(t + 1)!
We provide hints here not complete solutions.

This was an easy calculus problem once you got through the simple algebra substitution.

 

[help meeeeeeee]

It was left for YOU to figure out that it is -4 arctan(t) and not + 2 arctan(t + 1)!
We provide hints here not complete solutions.

This was an easy calculus problem once you got through the simple algebra substitution.

ok if its simple algebra as he say why did he fail to find -4 arctan(t). it's easy right how can u get a different answer than the real one..=thus its not easy. (provided u are good at math, which i believe he is)

 

[Steven G]

ok if its simple algebra as he say why did he fail to find -4 arctan(t). it's easy right how can u get a different answer than the real one..=thus its not easy. (provided u are good at math, which i believe he is)

I'm not saying that a mistake was or was not made. I will say that just because someone makes a silly computational mistake does not mean that the problem has to be hard.
I am 100% sure that if you gave me 100 very basic arithmetic problems I will not get every one correct as I will make silly mistakes. Does that make some of those problems hard? No, not at all.

 

[help meeeeeeee]

this ain't 100 problems doe, its only 1 and saying it's easy then failing at solving it looks kinda suspicious doesn't it

 

[Steven G]

this ain't 100 problems doe, its only 1 and saying it's easy then failing at solving it looks kinda suspicious doesn't it

I think the 'error' was done on purpose to keep you on your toes. The chances of getting the 1st problem wrong out of 100 is the same as getting any of the other 99 problems wrong.

 

[help meeeeeeee]

I think the 'error' was done on purpose to keep you on your toes. The chances of getting the 1st problem wrong out of 100 is the same as getting any of the other 99 problems wrong.

im 100% sure it wasnt on purpose, check his post, he edited it anyways this is nonsense and will not benefit me in any way for my test! thank you all for your precious time and have a good day!