Question

How do you integrate `1 / (x^5)`?

Answer 1

`-1/(4x^4)+c`

Explanation:

Integrate using the `color(blue)"power rule for integration"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(int(ax^n)dx=a/(n+1)x^(n+1))color(white)(2/2)|)))`

Express `1/x^5=x^-5`

`rArrintx^-5dx=1/(-5+1)x^(-5+1)+c`

`=-1/4x^-4+c=-1/(4x^4)+c`

where c is the constant of integration.