Need some assistance with integration

[Brownfractals]

Homework Statement

∫ x^(5)-2x^(2)-1/3x^(4) dx

Homework Equations

I am familiar with the power rule and how to split the expression into three separate expressions and then simplifying. I just can't seem to sort out my algebra for this problem.

xn dx = xn+1

n + 1 + C if n is NOT= -1
x-1 dx = ln|x|+ C

The Attempt at a Solution

Here is where i become stuck...Please show me a step by step process to solving the remainder of this problem; that way i can analyze it more deeply. Please Point out any things that seem wrong,i would REALLY appreciate the help given. :) :


∫ (x^5/3x^4 -2x^2/3x^4 -1/3x^4)dx = ∫ 1/3x -2x^(-2) -1/3x^(-4)dx = ∫ (x^2/6 + 2/x +1/9x^3) + C <------- This is the part where i become flabbergasted. . .Its simple I am sure but i just cannot see it. I was thinking about multiplying the whole expression by 18x^3 but i am not sure if that is correct.

 

[Tedjn]

Before we can give you help, can you clarify with parentheses what your integrand is? Is it (x⁵-2x²-1)/(3x⁴)? I ask, because it is difficult to read the problem and your work without parentheses.

 

[Mark44]

Also, when you write stuff like this

xn dx = xn+1

n + 1 + C if n is NOT= -1
x-1 dx = ln|x|+ C​

it's difficult to discern that xn means xⁿ or that x-1 means x^-1. At the very least, use ^ more consistently.