Question

How do you integrate `f(x)=x^3secx` using the product rule?

Answer 1

actually product rule is appliccabe for differentiation and not integration and if you want to integrate functions like these we use integration by parts

Explanation:

DIFFERENTIATION USING PRODUCT RULE `:`
given function `f(x)=x^3secx`
the product rule is given as `(uv)'=u'v+uv'` here `u=x^` and `v=secx`
substituting and differentiating we get
#f'(x)=secx(3x^2)+x^3(secxtanx) =secx(3x^2+x^3tanx)=x^2secx(3+xtanx)#
`:.f'(x)=x^2secx(3+xtanx)`