Original
Compute:
{{MATH_38}}
{{CMD_39}}
Here we will set
{{MATH_40}}
Then
{{MATH_41}}
Here, we are thinking in terms of differentials. We can solve for {{MATH_42}} to get
{{MATH_43}}
Using this equality, we can write
{{ENV_44}}
Notice that we have substituted in the new variable {{MATH_45}}, in both the integrand and in the limits of integration.
When we make the substitution we have to update the limits of integration to rewrite them in terms of the new substitution variable.
At this point, we can continue as we did before and write
{{MATH_46}}
{{CMD_47}}
{{CMD_48}}