What is #int 4 x^5 -7 x^4 + 3 x^3 -8 x^2 -4 x + 1 dx#?

2 Answers
Apr 13, 2018

#=> 2/3x^6 - 7/5x^5 +3/4 x^4 -8/3x^3 -2x^2 +x+C#

Explanation:

#int (4 x^5 -7 x^4 + 3 x^3 -8 x^2 -4 x + 1) dx#

#=4intx^5dx -7 int x^4dx + 3 int x^3dx - 8 intx^2 dx -4 int xdx +int dx#

#=4(x^6/6) - 7(x^5/5) + 3(x^4/4) -8(x^3/3) -4(x^2/2) + x+C#

where #C# is an arbitrary integration constant.

#= 2/3x^6 - 7/5x^5 +3/4 x^4 -8/3x^3 -2x^2 +x+C#

Apr 13, 2018

#2/3x^6-7/5x^5+3/4x^4-8/3x^3-2x^2+x+c#

Explanation:

#"integrate each term using the "color(blue)"power rule"#

#•color(white)(x)int(ax^n)dx=a/(n+1)x^(n+1);n!=-1#

#=4/6x^6-7/5x^5+3/4x^4-8/3x^3-4/2x^2+x+c#

#=2/3x^6-7/5x^5+3/4x^4-8/3x^3-2x^2+x+c#

#"where c is the constant of integration"#