# Recent content by Cacophony

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?