How do you integrate $int(3x^5-3)^(3/5)*15x^4 dx$ using substitution?

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Answer 1 · 2016-07-24T03:57:40

Let $u = 3x^5 - 3$ .

Then $(du)/dx = 15x^4 -> du = 15x^4dx -> (du)/(15x^4) = dx$

$=int(u)^(3/5) xx 15x^4 xx (du)/(15x^4)$

$=int(u^(3/5)) du$

$=(u^(3/5 + 1))/(3/5 + 1) + C$

$= (u^(8/5))/(8/5) + C$

$=5/8u^(8/5) + C$

$=5/8(3x^5 - 3)^(8/5) + C$

Hopefully this helps!

How do you integrate int(3x^5-3)^(3/5)*15x^4 dxint(3x^5-3)^(3/5)*15x^4 dx using substitution?