Explain to me the integration techniques?

[okkvlt]

Can somebody explain to me the integration techniques?

Also, say you have something like
x^8*5*2
so do i really need to simplify the integral 8 times just to get rid of the x^8 term? Is there a shortcut?

Also, i need some related rates practice problems. With answers so i can check myself.

 

[HallsofIvy]

Can somebody explain to me the integration techniques?

Is not uncommon for an entire semester course to be devoted to that!

Also, say you have something like
x^8*5*2
so do i really need to simplify the integral 8 times just to get rid of the x^8 term? Is there a shortcut?

What do you mean by "x^8*5*2"? If you mean (x^8)*5*2 that is just 10x^8 which has anti-derivative (10/9)x^9+ C. If you mean x^(8*5*2) that is just x^(160) which has anti-derivative (1/161)x^(161)+ C. I don't know what you mean by "simplify the integral 8 times".

Also, i need some related rates practice problems. With answers so i can check myself.

Get a good calculus book.

 

[okkvlt]

I got careless. By x^8*5*2 i actually meant x^8 times 5^x