Here's the question :
Evaluate the foll.intgral
[Int] 2 x^2 . cos (1/2 x^3 ) dx
I tried to do it by u-substitution and got this answer :
[4/3 x^3 . 4 sin (1/2 x^3 ) . 2 x^-2] + c
This does not look right.
Can someone pls show me how to do it?
well if you dont want to use substitution you can recognize from the differentiation of sine functions:
now lets look at your case:
looking at the trigonometry what do you differentiate to obtain:
well you can see that will give you the required cos function:
From here we can see that differentiating will give us almost the required answer.
Multiplying both side with 4/3 gives:
Now we just integrate both sides to obtain the required question: