Integration/antidifferentiation. x^4/4?

Question

x to the power of 4, divide four.

ie (x^4)/4

It's a very simple problem if you draw it on paper, but I can't for the life of me... Anyway, little help please?

Answer 1

Add 1 to the exponent and then divide by that number.
The exponent is 4
4 + 1 = 5
then divide by 5

(x^4)/4 dx = ((x^5)/5)/4 + C
= (x^5)/20 + C

Answer 2

You mean
∫(x^4/4)dx

Since x^4/4 = 1/4 x^4,
= ∫(1/4 x^4)dx

Since(if u is a constant) ∫ u f(x)dx = u ∫ f(x)dx,
= 1/4 ∫ x^4 dx

We know that ∫x^n dx = x^(n + 1)/(n + 1) + C, then
= 1/4 (x^5/5) + C

Thus,
∫(x^4/4)dx = x^5/20 + C

^_^