Find Integration of #(x^3)/(x^3) - 2x - 3# ???

2 Answers
Mar 15, 2018

#intx^3/x^3-2x-3dx=-x^2-2x+"C"#

Explanation:

Given: #intx^3/x^3-2x-3dx#

We can simplify the integral as:

#int1-2x-3dx#

#int-2x-2dx#

Next we integrate each term

#int-2xdx+int-2dx#

#int-2xdx=-(2x^2)/2=-x^2#

#int-2dx=-2x#

Therefore,

#int-2xdx+int-2dx=-x^2-2x+"C"#

Mar 23, 2018

#-2x-x^2+C#

Explanation:

We are given: #int(x^3/x^3-2x-3) \ dx#

We see that #x^3/x^3=1#, and the integral becomes:

#=int(1-2x-3) \ dx#

Combining like-terms, we get,

#=int(-2-2x) \ dx#

Now, we use the sum rule, and we can split the integral into,

#=int(-2) \ dx+int(-2x) \ dx#

#=-2x+(-x^2)#

#=-2x-x^2#

Now, we just need to add a constant, and we get,

#=-2x-x^2+C#