Question

What is the antiderivative of `lnsqrt( 5 x )`?

Answer 1

`I = (x(ln(5)+ln(x) - 1))/2 + c`

Explanation:

`I = intln(sqrt(5x))dx`

Using log properties

`I = 1/2int(ln(5) + ln(x))dx`

`I = (xln(5))/2 + 1/2intln(x)dx`

For the last integral say `u = ln(x)` so `du = 1/x` and `dv = 1` so `v = x`

`I = (xln(5))/2 + 1/2(ln(x)x - intx/xdx)`
`I = (x(ln(5)+ln(x) - 1))/2 + c`