well,
i'll start from the top
remember that (ab)^c=(a^c)(b^c)
2x^5+6x=2(x^5+3x)
the deritivive of (x^5+3x) is 5x^4+3
so therefor u=(x^5+3x)
du=5x^4+3 dx
so
∫(2)^3(x^5+2x)^3(5x^4+3)dx
∫8(x^5+2x)^3(5x^4+3)dx
8∫u^3du
[tex]8 \frac{u^{3+1}}{3+1} [/tex]
[tex]8 \frac{u^{4}}{4} [/tex]
[tex] 2u^{4} [/tex]
sub back
[tex] 2(x^5+3x)^{4} [/tex]
answer is [tex] 2(x^5+3x)^{4}+C [/tex]
the problem was you used the wrong 'u'
