What is #int x^4 + 9 x^3 -8 x^2 -3 x + 5 dx#?

1 Answer
Jan 21, 2016

#1/5x^5+9/4x^4-8/3x^3-3/2x^2+5x+C#

Explanation:

Use the rule:

#intx^ndx=(x^(n+1))/(n+1)+C#

Also, recall that multiplicative constants (like the #9# in #9x^3#) can be brought outside of the integral, but just stay and are multiplied in, and that various antiderivatives can be added.

Also, the antiderivative of a constant, like #5#, is simply #5x#. This is true since #5=5x^0#, to which the original rule can be applied.

The antiderivative of the given function is:

#x^(4+1)/(4+1)+(9x^(3+1))/(3+1)-(8x^(2+1))/(2+1)-(3x^(1+1))/(1+1)+(5x^(0+1))/(0+1)+C#

#=1/5x^5+9/4x^4-8/3x^3-3/2x^2+5x+C#