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

1 Answer
Jan 14, 2018

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)