What is the integral of x*sec^2x^2 dx?

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justaguide eNotes educator| Certified Educator

We have to find the integral of x*(sec x^2)^2

Let u = x^2

du/dx = 2x

=> x*dx = (1/2)du

Int [ x*(sec x^2)^2 dx]

=> Int [ (sec u)^2*(1/2) du]

=> (1/2) tan u + C

substitute u = x^2

=> (1/2) tan x^2 + C

The required integral is (1/2) tan x^2 + C

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