Which integral can I solve by substitution: cos(x²), x cos(x²), or x² cos(x²)?

[Natasha1]

I have been asked to state which one of the following 3 integrals I can solve using integration by substitution

(i) integral cos (x^2) dx

(ii) integral x cos x (x^2) dx

(iii) integral x^2 cos (x^2) dx

I would say that it is (ii) because x is the derivative of x^2 is that the correct answer or is there anything else I should add? Thanks in advance

 

[arildno]

That would be okay enough, I guess.

 

[Jameson]

Well, x isn't the derivative of $x^2$, but I know what you meant. Maybe you could also show how basic substitution fails on the other two.