Hi, I need someone's help to little bit teach me some Calculus 1 problems :)

Question

anonymous · Answer

the following resources are godsends

khan academy

patrickjmt

jaweria · Answer

I tried that but didnt help me that much

jaweria · Answer

homework

jaweria · Answer

$$\int\limits(8+x ^{3})^{5}3x ^{2}dx$$

jaweria · Answer

Evaluate. Assume u>0 when ln u appears

anonymous · Answer

notice that 
1) the integrand is expandable bu not easy.
2) is there something you might substitute in there and have its derivative also?

jaweria · Answer

we need to find u, and du

anonymous · Answer

there is no "u" in the given problem. only "x"

anonymous · Answer

do you find something that we can substitute in the integrand?

jaweria · Answer

but it says that Evaluate. Assume u>0 when LN u appears. ( Be sure to check by differentiating)

anonymous · Answer

yes. that is after the appropriate substitution

fibonaccichick666 · Answer

It is a method of integration called u substitution

jaweria · Answer

ok

jaweria · Answer

so can you help me solve this question?

fibonaccichick666 · Answer

yea give me a sec to write an example

jaweria · Answer

ok :)

fibonaccichick666 · Answer

http://www.educreations.com/lesson/view/for-jaweria/7579363/ This explains the u sub method

anonymous · Answer

in the integration example that you showed,
notice that the expantion of the binomial is the long part
so, we try to substitute that

jaweria · Answer

ok

fibonaccichick666 · Answer

do you understand the method? and what would you use as u in this question?

jaweria · Answer

no I m still struggling :(

fibonaccichick666 · Answer

ok where did you get lost in my explanation?

jaweria · Answer

like if you can explain me with numbers instead of words then I ll be fine

fibonaccichick666 · Answer

uhm, I don't understand

fibonaccichick666 · Answer

from mine, what is the derivative of sin(x)?

jaweria · Answer

cosx

fibonaccichick666 · Answer

alright so when you have $$\int sin(x)cos(x)dx$$
what is your u?

jaweria · Answer

cosx

fibonaccichick666 · Answer

why?

anonymous · Answer

that is fine. you can choose cos x as u too. 
next, what will be du?

anonymous · Answer

|dw:1367576718636:dw|
when we substitute "u" for some "x" , we are still integrating the same exact function but not the function is way simpler to manipulate.
after substitution, there should be no more "x" in the integrand.