- #1

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[tex]\int\frac{x^3e^{x^2}}{(x^2+1)^2}dx[/tex]

I have let u equal almost everything possible.

[tex]u=x^2[/tex]

[tex]d=2xdx[/tex]

[tex]u=e^{x^2}[/tex]

[tex]\ln u=x^2[/tex]

[tex]\frac{du}{u}=2xdx[/tex]

[tex]u=x^2+1 \leftrightarrow u-1=x^2[/tex]

[tex]\ln u=\ln{(x^2+1)}[/tex]

[tex]\frac{du}{u}=\frac{2xdx}{x^2+1}[/tex]