Solve below?

Question

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

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Answer 1 · 2017-08-24T13:11:00

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

#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.