Question

Solve below?

`int_1^2ln(3x^2)dx`

Answer 1

`int_1^2ln3x^2dx = -2+ln48`

Explanation:

`ln3x^2 -= ln3+lnx^2 -= ln3+2lnx`

`therefore intln3x^2dx = intln3dx + 2intlnxdx = xln3 + 2intlnxdx`

For `intlnxdx`, use integration by parts.

`intlnxdx = intlnx*1dx`

Let `f(x) = lnx rArr df = 1/xdx`

And `dg = dxrArr g(x) = x`

Then `intlnx*1dx = xlnx - int1dx = xlnx-x +"constant"`

`therefore int_1^2 ln3x^2dx = [xln3 +2xlnx-2x]_1^2`

Evaluating the limits will yield the given answer. I shall leave that up to you.