Recent content by emmaerin

I completely forgot to bring down the 5 - that was the whole problem! Such a silly mistake, thanks for pointing it out!

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.) \int \frac {5x^2 - 20x +45}{(2x+1)(x-2)^2}\, dx Homework Equations 5x^2 - 20x +45 = 5 (x^2 -4x +9) The Attempt at a Solution I'm able to come up with an...

So is the final answer -1/9 t e ^(-9t) + 1/81 e ^(-9t) + C ?

You're completely right - I accidentally switched v and dv, thanks for pointing that out!

Homework Statement Evaluate the integral. (Use C for the constant of integration.) ∫te ^ (-9t) dtHomework Equations ∫udv = uv - ∫vdu u=t dv= e ^ (-9t) dt du=dt v=(-1/9) e ^(-9t) The Attempt at a Solution = -1/9 te^(-9t) - ∫-1/9 e ^(-9t) dt Second Integral...

1 / (2 * (1 - x^2)^1/2 ) ?

This is where I am so far, using the chain rule. Could someone help me figure out where I'm going wrong/what comes next? Thanks! y = arctan ( (1+x)/(1-x) )^1/2 1. y' = 1/ (1 + (1+x)/(1-x)) * 1/2 ( (1+x)/(1-x) )^-1/2 * ( (1-x)(1) - (1+x)(-1) ) / (1-x)^2 2. y' = (1-x)/2 * 1/2 (...

Could you please explain further? Where did the cos come from? (I apologize if this is basic; I've missed a week's worth of classes due to a lung infection and I'm desperately trying to catch up.)

Thank you! And yes, that is the correct function.

Homework Statement Find the derivative of the function. Simplify where possible. y= arctan ( (1+x)/(1-x))^1/2 Homework Equations d/dx (arctan x) = 1/(1+x^2) The Attempt at a Solution I'm really not sure where to even begin, so any help would be greatly appreciated!