Changes

:<big><math>\int\frac{2x}{x^2+3}dx=\int\frac{1}{u}du</math></big>

:<big><math>\int\frac{2x}{x^2+3}dx=\int\frac{1}{u}du</math></big>

We can rewrite the intergal this way due to the subsitution of the x terms with the u terms.

We can rewrite the integral this way due to the subsitution of the x terms with the u terms.

Now we can solve the intergral in terms of u.

Now we can solve the integral in terms of u.

:<big><math>\int\frac{1}{u}du=ln|u|+c</math></big>

:<big><math>\int\frac{1}{u}du=ln|u|+c</math></big>