Find the integral

• Jan 29th 2013, 04:34 PM
kuppina
Find the integral
Hey everyone I have a math question that I really need help on:

Find the integral.
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!

• Jan 29th 2013, 07:46 PM
chiro
Re: Find the integral
Hey kuppina.

What is the definition of the integral? (I think your attachment if you used it didn't come through)
• Jan 29th 2013, 08:13 PM
kuppina
Re: Find the integral
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
• Jan 29th 2013, 08:20 PM
chiro
Re: Find the integral
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.