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## Main Question or Discussion Point

I have found that the U-Subsitution procedure can basically be completed in one step as is here:

[tex]\int f(g[x]) dx = \frac{\int f(t) dt}{g'(x)} + C[/tex]

and then replacing t with g(x) once the integral of f(x) is found.

Example: Say we have:

[tex] \int e^{x + 3x^{2}} dx [/tex]

Using the other formula, we get

[tex] \frac{e^{x + 3x^{2}}}{6x + 1} + C[/tex]

which is actually the same equation as we would have gotten if we used U substitution

[tex]\int f(g[x]) dx = \frac{\int f(t) dt}{g'(x)} + C[/tex]

and then replacing t with g(x) once the integral of f(x) is found.

Example: Say we have:

[tex] \int e^{x + 3x^{2}} dx [/tex]

Using the other formula, we get

[tex] \frac{e^{x + 3x^{2}}}{6x + 1} + C[/tex]

which is actually the same equation as we would have gotten if we used U substitution