How do you integrate int(5x^4+5)^(2/3)*20x^3 dx using substitution?

1 Answer
Jul 20, 2016

Let u = 5x^4 + 5, then (du)/dx = 20x^3 -> du = 20x^3dx -> dx = (du)/(20x^3)

=int(u^(2/3)) xx 20x^3 xx (du)/(20x^3)

=int(u^(2/3)) xx cancel(20x^3) xx (du)/cancel(20x^3)

=(u^(2/3 + 1))/(2/3 + 1) + C

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

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

=3/5(5x^4 + 5)^(5/3) + C

Hopefully this helps!