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