[tex]\displaystyle \int \frac{2x^7}{x^4 + 4} \, dx[/tex]
Let [tex]u=x^4 + 4[/tex] and [tex]du=4x^3\,dx[/tex]. Then
[tex]\displaystyle \int \frac{2x^7}{x^4 + 4} \, dx = \frac14 \int \frac{2(u-4)}u \, du \\\\ ~~~~~~~~ = \frac12 \int \left(1 - \frac4u\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(u - 4\ln|u|\right) + C \\\\ ~~~~~~~~ = \frac12 \left(x^4 +4 - 4\ln\left|x^4+4\right|\right) + C \\\\ ~~~~~~~~ = \boxed{\frac{x^4}2 - \ln\left(x^4+4\right)^2 + C}[/tex]
