integration help plz

[Maz]

hey, could someone please help me do this question?
i have absolutely no idea how to do the integration of this:
(2x+1)^4   and 12/(1-3x)^2
i really don't understand the book when it explains it...

thankyou so much in advance

[TheAspiringDoc]

this might help: https://au.answers.yahoo.com/question/index?qid=20110419071708AAmnMUs

[cosine]

hey, could someone please help me do this question?
i have absolutely no idea how to do the integration of this:
(2x+1)^4   and 12/(1-3x)^2
i really don't understand the book when it explains it...

thankyou so much in advance

There is a rule for integration when you have linear expressions raised to any power, except for 1, that is:



So in your example, a = 2, b = 1 and n = 4:

=

For the second example, you can use the same rule but you must raise the expression so that it remains not in fraction form, and you do this by negating the power:



Now, your a = -3, b = 1 and n = -2 and plug these into the rule I stated above:



Hope this helps you a bit, let me know if you need further clarifications!

[TheAspiringDoc]

May I ask how you know that rule cosine?
Do you simply have to remember it or is there an intuitive method that you used?

[Splash-Tackle-Flail]

I'm not cosine, but the way I think of it is that in normal polynomial integration, we know that



The second step uses the property in differentiation of the chain rule.

So in integration you would divide by in a sort of reverse chain rule, giving the rule cosine wrote.

If you want to do your own research or look for better examples, google u substitution (which is rule is a form of), which you do in spesh anyway

[wyzard]

I'm not cosine, but the way I think of it is that in normal polynomial integration, we know that



The second step uses the property in differentiation of the chain rule.

So in integration you would divide by in a sort of reverse chain rule, giving the rule cosine wrote.

If you want to do your own research or look for better examples, google u substitution (which is rule is a form of), which you do in spesh anyway

The substitution method is sure really handy in integration  Unfortunately it is not taught in methods but only in specialist maths

[Maz]

thanks guys