Recent content by LilTaru

After looking on the internet for a sample problem like this... I have found I am retarded... Figured out the problem: equated the coefficients wrong! Thank you all for your help! :P

Main equation: 1 = (Ax + B)(x2 - 2\sqrt{}2*x + 4) + (Cx + D)(x2 + 2\sqrt{}2*x + 4) Set x = 0: 1/4 = B + D Set x = sqrt(8): 1 = 8*sqrt(2)A + 8B + 40*sqrt(2)C + 20D Set x = sqrt(2): 1 = -2*sqrt(2)A - 2B + 28*sqrt(2)C + 14D Set x = 3*sqrt(2): 1 = 30*sqrt(2) + 10B + 102*sqrt(2) + 34D...

I've tried solving the system of equations but cannot seem to get it not matter how hard I try... can someone please help me solve the system? After that I know how to do the integral.

So I got it to x/(1 + sin(x)) = x(1 - sin(x))/(cos2(x)) but now I am stuck again... D:

No indefinite and yeah looks complex to me...

Evaluate an Integral - No Clue! Homework Statement \int x/(1 + sin(x)) dx Homework Equations The Attempt at a Solution I don't know what rules to use or what approach to take! Please help!

But I thought when you put in values of x it should make one of the factors be 0 so that you can solve for the other one?

Okay... I tried to solve for the constants but I am stuck... I get this equation: 1 = (Ax + B)(x2 - 2*sqrt(2)*x + 4) + (Cx + D)(x2 + 2*sqrt(2)*x + 4) I can't see how to solve this either by finding an x where the factors are zero or by solving a system of equations... How can I turn this...

Yeah. This was my first approach but if you plug in the value of a = 4, it seems the two factors of the hints never equal 0... Maybe this is just me.

How would I do that?

Homework Statement \int dx/(x4 + 16) Homework Equations Hint: With a>0, x4 + a2 = (x2 + \sqrt{}2ax + a)(x2 - \sqrt{}2ax + a) The Attempt at a Solution I've plugged this into the equation, which leaves me with: \int dx/[(x2 + \sqrt{}2ax + a)(x2 - \sqrt{}2ax + a)] But now I...

Oh, okay! This makes a lot of sense now! Thank you so much!

Or do I differentiate f first and plug sin x into the already differentiated function?

Oh. So I just differentiate the actual function? That sounds a lot easier. To clarify: when sin x is a limit, I plug in sin x into f and then differentiate the function, then multiply all of that by cos x? And in (e) do we treat the x's in the function as a constant?

Homework Statement Differentiate the following functions with respect to x. a) \int (t2 + cos(t7))/(1 + t4) dt [0, x] b) \int (t2 + cos(t7))/(1 + t4) dt [2, x] c) \int (t2 + cos(t7))/(1 + t4) dt [0, sin x] d) \int (t2 + cos(t7))/(1 + t4) dt [x, sin x] e) \int (x2 + cos(t7))/(1...