Question

Integrate by parts. See below.Need help as to process.

Answer 1

\[\frac{ x }{ \sqrt{5+4x} }dx\]

Answer 2

Let u =x and dv = (5+4x)^(-1/2) dx

Answer 3

I did that

Answer 4

So the anti derivative of (5+4x)^(-1/2)is 2(5+4x)^1/2?

Answer 5

yup

Answer 6

Hold on

Answer 7

1/2 not 2 in the front. hehehe

Answer 8

Sorry why 1/2?

Answer 9

Is it 2 divided by 4 because of the 4x?

Answer 10

\[\int \dfrac{1}{\sqrt{5+4x}}dx\]
let u = 5+4x --> du = 4dx--> dx = du/4
\[\int \dfrac{1}{\sqrt{5+4x}}dx =\dfrac{1}{4}\int u^{-1/2} du = \dfrac{1}{4}*2\sqrt u= \dfrac{1}{2}\sqrt{5+4x} \]

Answer 11

So that would become \[\frac{ 2 }{ 9 }(5+4x)^{3/2}\]

Answer 12

Soory not 4/9 but 1/3

Answer 13

that is v, right?
so that you have
u = x dv = ...
du = dx v = \(\dfrac{1}{2}\sqrt {5+4x}\)
now combine to get
\(uv -\int vdu\)

Answer 14

\[2x*(5+4x)^{1/2}-1/3(5+4x)^{3/2}+C\]

Answer 15

ok, let check by wolfram http://www.wolframalpha.com/input/?i=int+%28x%2F%28sqrt%285%2B4x%29%29dx

Answer 16

http://www.wolframalpha.com/input/?i=int+%28x%2F%28sqrt%285%2B4x%29%29dx