Question

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

I got to here and then got stuck u=5x^4+3 du=x^5+3x+C ∫(2x^5+6x)^3 u 1/(x^5+3x+C) ∫(x^5+3x)^3 u

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 (u^(3+1))/(3+1)`

`8 (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'