Find the integral

Hey everyone I have a math question that I really need help on:

Find the integral.

http://edugen.wileyplus.com/edugen/s...=1359487571347

This equation was from my homework and the correct answer is ((5x^4+6)^3/2)/30. I understand how you get the numerator but I do not know how the denominator ends up being 30? Can someone explain this concept to me.

Thank you!

Hey kuppina.

What is the definition of the integral? (I think your attachment if you used it didn't come through)

Quote:

---

Originally Posted by chiro

Hey kuppina.

What is the definition of the integral? (I think your attachment if you used it didn't come through)

---

Sorry Chiro!

It is the integral of (x^3)(sqrt(5x^4+6)dx

Using the substitution u = 5x^4 + 6 we get du/dx = 20x^3 or du = 20x^3*dx.

This gives us a new integral of 1/20 * 20 * x^3 sqrt(u) * dx = 1/20 * sqrt(u)du.

Now integral 1/20*sqrt(u)du = 1/20*2/3*u^(3/2) + C but u = 5x^4 + 6 so the full integral is

1/20*2/3*(5x^4 + 6)^(3/2) + C = 1/30*(5x^4 + 6)^(3/2) + C.