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maxfails
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it seems you can't use the property ln x^n = n ln x.
I'm thinking there's integration by parts involved but not sure.
I'm thinking there's integration by parts involved but not sure.
maxfails said:I'm thinking there's integration by parts involved but not sure.
ln x^{n} = t
x = e^{t}
dx = e^{t} dt
so initial eqn becomes
[tex]\int t^n e^t dt[/tex]
maxfails said:it seems you can't use the property ln x^n = n ln x.
I'm thinking there's integration by parts involved but not sure.
The general formula for integrating (ln(x))^2 is ∫ (ln(x))^2 dx = x(ln(x))^2 - 2xln(x) + 2x + C.
Yes, (ln(x))^2 can be simplified to ln(x^2) before integrating.
To integrate (ln(x))^2 using substitution, let u = ln(x), then du = 1/x dx. The integral becomes ∫ u^2 du, which can be easily solved using the power rule.
Yes, you can also integrate (ln(x))^2 by parts. Let u = (ln(x))^2 and dv = dx, then du = 2ln(x)/x dx and v = x. The integral becomes ∫ (ln(x))^2 dx = x(ln(x))^2 - 2∫ xln(x)/x dx. The second term can be simplified to -2∫ ln(x) dx, which can then be solved using substitution.
Yes, most scientific calculators have a built-in function for integrating (ln(x))^2. Simply input the function and the limits of integration to get the result.