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Question
The indefinite integral: integral of (((x^(1/3) + 1)^4) / (x^(2/3)))dx equals
Basically, you want ∫ [x^(1/3) + 1]^4 / [x^(2/3)] dx.
Let u = x^(1/3), then du = 1/[x^(2/3)] dx.
It is noted that [x^(1/3) + 1]^4 = (u+1)^4 and [x^(2/3)] dx = du,
so the integral is now ∫(u+1)^4 du.
The answer to that is {[(u+1)^5]/5} + K. In this, put in u = x^(1/3),
and that will be the answer in terms of x. That can be written as (u+1)^5/5 + K
since first we do what is in the parenthesis, then take the power, then divide by 5,
and then add on K to that by mathematical rules.
They are the order in which things are done
1. Powers,
2. Multiplication/Division, and
3. Addition/Subtraction.
Parenthesis take precedence over the above.
Have a great day and dive into that math!
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