Solve below?

int_1^2ln(3x^2)dx

1 Answer
Aug 24, 2017

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.