Question

How do you find the indefinite integral of `int (4x^-5) dx`?

Answer 1

`-1/x^4+C`

Explanation:

First pull out the constant using `intaf(x)dx=aintf(x)dx`:

`int(4x^-5)dx=4intx^-5dx`

Now, use the rule for integrating functions of `x` such as these: `intx^ndx=x^(n+1)/(n+1)+C`

Thus

`4intx^-5dx=4(x^(-5+1)/(-5+1))+C=4((x^-4)/(-4))+C=-1/x^4+C`