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?

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?

anonymous · Answer

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

anonymous · Answer

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

mathslover · Answer

Perfect! Got it.

Thanks!

anonymous · Answer

YW :)