Question

How do you evaluate the indefinite integral `int (6x^7)dx`?

Answer 1

`int(6x^7)dx = (3x^8)/4 + C`

Explanation:

For this indefinite integral we can apply the power rule.

The power rule states: `intx^ndx = (x^(n+1))/(n+1) + C`

So, when we plug in our values we get: `int(6x^7)dx = (6x^(7+1))/(7+1)`

`= (6x^8)/(8)`

`= (3x^8)/4`

`= (3x^8)/4 + C`

Answer 2

`3/4x^8+c`

Explanation:

`"integrate using the "color(blue)"power rule"`

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

`rArrint(6x^7)dx`

`=6/8x^((7+1))+c=3/4x^8+c`

`"where c is the constant of integration"`