# Search results

1. ### Integrals using long division

Homework Statement ∫(2x+1)/(x²+2x+1)(x²+x+1) Homework Equations none The Attempt at a Solution I've foiled this out to look like: ∫(2x+1)/(x^4+3x³+4x²+3x+1) I'm trying long division here but it's getting really ugly really fast. Should I foil this out in the first place or...

Ok, guess i'll try something else. Thanks

Homework Statement for the following integrals, am I allowed to break them up like so: 1. ∫(1)/(sqrt(16-9x²)³) dx = ∫(1)/(√16)³ · ∫(1)/(√-9x²)³ dx 2. ∫(x²)/(sqrt(x²-9)) dx = ∫(x²)/(√x²) · ∫(x²)/(√-9) dx 3. ∫(1)/(x²(sqrt(a²+x²))) dx = ∫(1)/(x²) · ∫(1)/(√a²) · ∫(1)/(√x²) dx...
4. ### The power rule and the chains rule

Homework Statement How do I know for sure when to use the power rule instead of the chain rule and vice versa? Homework Equations The Attempt at a Solution
5. ### Integrating a complex ln

Homework Statement integrate:13((4^x)+(3^x))dx Homework Equations The Attempt at a Solution I know the solution is 13((4^x)/ln(4) + (3^x)/ln(3)) + C Can someone explain to me how this works? I don't know where the ln's are coming from. How would I differentiate this back to...
6. ### Help with a derivative

Homework Statement derivative of: (14x^2)/sqrt(1-x) Homework Equations The Attempt at a Solution I am at this point at finding the derivative: (28x(sqrt(1-x))+((7x^2)/sqrt(1-x))/(1-x) I am confused about the next step because don't know how it's derived from the previous...
7. ### 4th derivative of cos(2x)

Ok cool but what rule did you use there?
8. ### 4th derivative of cos(2x)

Homework Statement see title. Homework Equations no The Attempt at a Solution Ok so the solution is 16cos(2x) but I'm not sure how it is derived to that. I've tried the product rule but it's not working for me. What rule or rules do I use to get this solution?
9. ### A couple of integration problems

I'm not following. What do you mean reduced to lowest terms?
10. ### A couple of integration problems

do I simplify the first one aswell? Cause someone said I didn't have to.

0 right
12. ### A couple of integration problems

so basically: (0-1)-(0-1)?
13. ### A couple of integration problems

Homework Statement a) S(4 is higher limit, 0 is lower limit) (x^4 - x^2 + 1)dx b) S(pi is higher limit, -pi is lower limit) (cosx + sinx)dx Homework Equations The S is the integration sign The Attempt at a Solution a) = ((x^5)/5)-((x^3)/3)+x I(4 high, 0 low) =...
14. ### Integrating e^7x

What happen's to du? Why does it dissapear in the solution?
15. ### Integrating e^7x

Homework Statement S e^7x Homework Equations no The Attempt at a Solution Ok so I am using U-substitution for this problem but I don't know what to do next. u = 7x, du = 7dx How do I integrate e^u*du?
16. ### Calculating indefinite integrals

Homework Statement a) S 13(4^x + 3^x)dx b) S (cosx + sec^2x)dx c) S (3-(1/x))dx d) S e^(7x)dx Homework Equations The S is supposed to be the integration sign The Attempt at a Solution Are these correct or at least close? a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C b) =...
17. ### Taking 2nd, 3rd and 4th derivatives

Homework Statement a) d^2/(dx^2): ln(x+1) b) d^3/(dx^3): x^7 + 4x^6 - x^2 c) d^2/(dx^2): 1/(x + 1) d) d^4/(dx^4): cos(2x) Homework Equations none The Attempt at a Solution Can someone tell me if these are right? a)= -(1/(x + 1)^2) b)=210x^4 + 480x^3 c)= (2/(x + 1)^3) d)=...
18. ### Limits to infinity with natural logs

Ignore my last post I got confused, this isn't a derivative
19. ### Limits to infinity with natural logs

I think I know how to do the first one by applying the chain rule: limit to infinity ((lnx)^5)/(x)= (5(lnx)^4)*(1/x)/(x)= 5(lnx)^4*0/(x)= 0 Is that valid?
20. ### Limits to infinity with natural logs

So basically the limit is then 28/18?

cool beans
22. ### A quick derivative question

Homework Statement What is the derivative of 14x^2? Homework Equations The Attempt at a Solution Do i bring the 2 in front to get 28x? Or do I use the chain rule?

1/1 ?
24. ### Limits to infinity with natural logs

ok so it will be ((28lnx)/x)/((18lnx)/x) = 0/0 = DNE?
25. ### Limits to infinity with natural logs

So would the second problem look something like this: 28lnx/18lnx?
26. ### Limits to infinity with natural logs

I'm not allowed to use L'Hopital, and I will change #2
27. ### Limits to infinity with natural logs

Homework Statement I'm having trouble calculating these limits. Homework Equations none The Attempt at a Solution 1. lim.......((lnx)^5)/(x)= x->infinity (((lnx)^5)/x)/(x/x)= (((lnx)^5)/x)/1= How do I calculate from here? 2.lim .......(14lnx^2)/(6lnx^3)=...
28. ### Calculating limits to infinity

No, i meant ((lnx)^5)/(x)
29. ### Calculating limits to infinity

Oh, so how would i calculate it then?
30. ### Calculating limits to infinity

I thought you could do that with natural logs?