Question

INTEGRATE 5x(sqrt(x+4))

Answer 1

\[\int\limits_{}^{}5x(\sqrt{x+4})\]

Answer 2

Oh ok now I remember what to do.
This is one of those tricky ones. It's a simple u-sub

Answer 3

\[\Large\rm u=x+4\]

Answer 4

Sub. u=sqrt(x+4)

Answer 5

\[\Large\rm \int\limits5\color{orangered}{x}\sqrt{\color{royalblue}{x+4}}~\color{green}{dx}\]You will have 3 things you need to replace.

Answer 6

ya or you can do that also^

Answer 7

i did that. I ended up with\[\int\limits_{}^{}5(u-4)u ^{\frac{ 1 }{ 2 }}\]

Answer 8

Ok good!
Now distribute your u^(1/2)
and integrate as you normally would!
power rule to each term

Answer 9

i ended up with\[2u ^{\frac{ 5 }{ 2 }}-\frac{ 40 }{ 3}u ^{\frac{ 3 }{ 2 }}\]

Answer 10

but then it differs by far from the wolfram answer, and its not good for our discussion here, because I really do not know what to say to the other guys now.

Answer 11

No it's the same as wolfram's solution.
You just have to tweak it.

Answer 12

So if we factor a 2/3 and u^{3/2} out of each term we get,\[\Large\rm \frac{2}{3}u^{3/2}(3u-20)\]Lemme do that in my head really quick.. make sure I didn't goof up..

Answer 13

Yah I think that's right.
Then undoing our substitution gives us,\[\Large\rm \frac{2}{3}(x+4)^{3/2}(3(x+4)-20)\]Which simplifies a little bit further to match things up right?

Answer 14

It can be tough to check your answers sometimes,
wolfram and even textbooks tend to `over simplify` things.

Answer 15

u r damn ryt man. have bn trying for hours!

Answer 16

oh good we figured it out \c:/ heh

Answer 17

cheers!