Does anybody know the best way to solve this equation?

Question

The indefinate integral (or anti derivitave) of

x^4 Sqrt[5 + x^5] dx

Thanks alot for any help

Answer 1

notice d/dz of sqrt (5+x^5) is .5*(5+x^5)^-.5 * 5x^4

so basically x^4 is a chain rule derivative of the inside of your other expression. Let u = 5+x^5
du = 5*x^4 dx

so x^4(dx)= 1/5 * du

so you have 1/5 sqrt u du
which you can go from there

Answer 2

I = ∫ x^4 / (5 + x^5)^(1/2) dx
Let u = 5 + x^5
du = 5x^4 dx
du / 5 = x^4 dx
I = (1 / 5) ∫ u^(1/2) du
I = (2 / 15) u^(3/2) + C
I = (2 / 15) (5 + x^5)^(3/2) + C

Answer 3

use chain rule...

else the fastest way is probably to ask ur tutor

Answer 4

http://mathworld.wolfram.com/

Answer 5

CHRIST MOUNTAIN FOR SQUIRTING (GIVE HIM FIVE WITH FIVE CHRIST MOUNTAIN) TO DX "youknowhim?"