Question

Starting Integral Calculus

Indefinite Integral (Algebra of Indefinite Integral)

If \(\int f(x) dx = F(x) + C\) , then \(\int f(ax+b) dx = \cfrac{1}{a} F(ax+b) + C \)

Is there any way to prove it?

Answer 1

yep there is :)
for example :-
differentiate both side w.r.t X

Answer 2

(1/a F(ax+b) ) '
= 1/a (ax+b )' F(ax+b)'
=1/a *a * F(ax+b)' = F(ax+b)'

Answer 3

Perfect! Got it.

Thanks!

Answer 4

YW :)