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

Jan 14, 2018

DIFFERENTIATION USING PRODUCT RULE $:$
given function $f \left(x\right) = {x}^{3} \sec x$
the product rule is given as $\left(u v\right) ' = u ' v + u v '$ here u=x^ and $v = \sec x$
f'(x)=secx(3x^2)+x^3(secxtanx) =secx(3x^2+x^3tanx)=x^2secx(3+xtanx)
$\therefore f ' \left(x\right) = {x}^{2} \sec x \left(3 + x \tan x\right)$