# Need some assistance with integration

## 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 cant 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 im 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.

Last edited:

## Answers and Replies

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
Mentor
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.