How to integrate this?

[Lost]

I am looking at the explanation to a problem, and I am really confused toward the end of this solution.

I understood everything till they showed

"Integrate with respect to u"

How did they integrate that? My mind is so boggled...

 

[Lost]

To show you guys what the problem was initially....

 

[wjm11]

To show you guys what the problem was initially....

You did not evaluate the integral correctly. You started with u^(1/3). The exponent needed to increase by 1, so: (1/3) + (3/3) = 4/3.

Next, consider the coefficient of the u term: 1/2. The integrated expression has a coefficient also, which we can just call "x" to start with.

When we take the derivative of "xu^(4/3) + C", we have to end up with "(1/2)u^(1/3)", right? So the derivative of "xu^(4/3) + C" (using the power rule) will equal (4/3)(x)(u^(1/3)). Therefore, (4/3)(x) must equal (1/2):

(4/3)(x) = (1/2)
x = 3/8

Make sense?

Alternatively, you could move the (1/2) out in front of the integral as you did. Then when you integrate u^(1/3), you get (u^(4/3))/(3/4). So,

(1/2)[(u^(4/3))/(3/4)] = (3/8)(u^(4/3))

 

[Lost]

Ohhhh I see! Thanks so much. Got it. =)