Advanced Calculus HELP!

[katmz]

We need help with this as soon as possible. Below you will find the problem. We know the answer is E, however, we keep getting C. Can anyone help us with the process?

 

[JohnZ]

using partial fraction decomposition
1/(x^2+4x) = 1/(x*(x+4)) = A/x+B/(x+4)
both sides time x*(x+4),get
1=A*(x+4) + B*x

 

[stapel]

We need help with this as soon as possible. Below you will find the problem.

. . . . .\(\displaystyle \displaystyle{\int\, \frac{dx}{x^2\, +\, 4x}\, =}\)

We know the answer is \(\displaystyle \displaystyle{\int\, \frac{dx}{4x}\, -\, \int\, \frac{dx}{4(x\, +\, 4)} }\), however, we keep getting \(\displaystyle \displaystyle{\int\, \frac{dx}{x}\, -\, \int\, \frac{dx}{x\, +\, 4} }\).

Please reply showing your steps, so we can help you find your errors, if any.

Please be complete. Thank you!

 

[fcabanski]

https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/PartialFrac.html

Why is the scan so dark?