Practice question · Select all that apply
Select every integral for which u = x^3 + 2 is a productive substitution.
Hints
- The derivative of x^3 + 2 is 3x^2; a constant multiple of it is good enough.
- An x or an x^2 is not the same thing, check the power carefully.
Show the answer
- A. 3x^2 (x^3 + 2)^5 dx
- B. x^2 times the square root of (x^3 + 2) dx
- C. x^2 e^(x^3 + 2) dx
Why
Options 1, 2 and 4 all carry an factor, which is up to the constant 1/3, so the substitution closes. Option 3 has no such factor at all, and option 5 offers x rather than , a missing variable factor cannot be fixed by pulling out a constant.
Practise Integration by Substitution
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