Question

Evaluate using substitution ∫(2x^5+6x)^3(5x^4+3)dx where b=0 and a=-1

Answer 1

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
$8 \frac{u^{3+1}}{3+1}$
$8 \frac{u^{4}}{4}$
$2u^{4}$
sub back
$2(x^5+3x)^{4}$

answer is $2(x^5+3x)^{4}+C$

the problem was you used the wrong 'u'