Theorem\(\qquad\quad\) If&nbsp;\(u = g(x)\) is a differentiable function whose range is an interval \(I\) and \(f\) is continuous on \(I\), then
\(\int f'(g(x)) g'(x) \mathrm{d}x = \int f'(u) \mathrm{d}u\) 
This method of integration is helpful in reversing the chain rule.
Possible conditions seen when the method of substitution may be applicable:
<ul class="bullet-list"><li><div class="list-item-content">A complicated expression with the "inside", \(g(x)\), and</div></li><li><div class="list-item-content">the derivative of the complicated expression is seen somewhere in the integrand.</div></li></ul>

**Theorem**\(\qquad\quad\) If \(u = g(x)\) is a differentiable function whose range is an interval \(I\) and \(f\) is continuous on \(I\), then

\(\int f'(g(x)) g'(x) \mathrm{d}x = \int f'(u) \mathrm{d}u\)







This method of integration is helpful in reversing the chain rule.

Possible conditions seen when the method of substitution may be applicable:

A complicated expression with the "inside", \(g(x)\), and

the derivative of the complicated expression is seen somewhere in the integrand.

Integration by Substitution

Integration by Substitution