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weeeeeb [17]
4 years ago
14

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

Mathematics
1 answer:
malfutka [58]4 years ago
6 0
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
<span>∫(2)^3(x^5+2x)^3(5x^4+3)dx
</span>∫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'
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