Integration with U Substitution

[mattt874]

Can you Resolve the following ?4x^3/(x^4+1).dx and show the working so I may understand how it is done:

I have:

u = x^4+1
du/dx = 4x^3

Then I am not sure how to proceed or where to go. I want to think that du = 1/4x^3 but i am not sure that is right.

leaving me with

?(4x^3/u).1/4x^3 dx

Matt

 

[galactus]

You have the right sub. Remember, you can not mix up u's and x's.

That is, after the sub is made, there should be no more x's...all u's.

\(\displaystyle u=x^{4}+1, \;\ du=4x^{3}dx\)

Make the subs:

\(\displaystyle \int\frac{1}{u}du\)

That's it. integrate and resub.

 

[mm391]

Hi,

Just read your post and I am having a similar issue with this:

(2x+3/(2x^2+6x+1)^1/2

I have used y insteard of u so:

y = 2x^2+6+1
du/dx = 4x + 6
so dx = du/4x+6

but I am not sure how it goes on from here.

 

[SigepBrandon]

hey MM!

welcome,

First, in the future, you might want to create a new post when asking a new question... but to address yours-

did you mean:

u = 2x^2+6x+1
so,
du= 4x + 6 dx

notice that du is twice that of the numerator, so you need to multiply the integral by 1/2.. the new integral then is:

\(\displaystyle \frac{1}{2}\int \frac{1}{\sqrt{u}} du\)

try it from there!