Evaluate.
Integral s^5(2+s^6)^8ds

Question

Evaluate.
Integral s^5(2+s^6)^8ds

lukecrayonz · Answer

$$\int\limits_{?}^{?}s^{5}(2+s^{6})^{8}$$

turingtest · Answer

what u substitutions have you tried?

myininaya · Answer

Not always, but usually a good algebraic substitution to start with is trying let u equal the inside of a nasty part ( if that makes sense)

lukecrayonz · Answer

None since I have never learned this haha, this is my first question!:-)

johnweldon1993 · Answer

Oh, okay...well, do you see a function in this integral where the derivative of that function is also shown?

lukecrayonz · Answer

It's kinda like f(g(x))g'(x) if that makes sense lol

johnweldon1993 · Answer

Yeah something like that lol...so here I'll kind of give you this one...

A good place to start, is to try an take the innermost function and see if the derivative (or some variation of it) is also shown in the integral...so here...

The innermost would be (2 + s^6)   what is the derivative of that function?

lukecrayonz · Answer

6s^5

lukecrayonz · Answer

@myininaya @TuringTest what about for this one?
$$\int\limits_{a}^{b}\frac{ lnx^{2} }{ 5x }dx$$

myininaya · Answer

what is the derivative of ln(x)?

lukecrayonz · Answer

1/x

myininaya · Answer

you should see 1/x in your problem

myininaya · Answer

also I'm guessing that square is on ln(x) and not just the x
am i wrong or right?