Question

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

Answer 1

`=> 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`

Answer 2

`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"`