Efficient Integration: Substitution Method for 2x sec^2(x^2) dx

[rugapark]

the question is $$\int 2x sec^2 (x^2) dx$$

do i sub u= sec (x^2) ?

I so far have got to trying to sub u= sec(x^2) and getting du= 2 (sec x^2 tan x^2)... i have a strong feeling i fudged the "du" part. hmm.

 

[rocomath]

$$u=x^2$$

$$du=2xdx$$ which you have! What is the anti-derivative of $$\sec^2 x$$ ?

 

[rugapark]

oh right, so I've got du=2xdx,

intergral sec^2 u du

= tan u + c

sub back u=x^2

=tan x^2 +c

how does that look?

 

[Dick]

It looks just fine.