For example, I have the integral ∫xln(x^2)dx. Would it be better to use parts?
So far, I have tried: u= x^2
I came up with the new integral of 1/2∫ln(u)du... I am not sure what the next step is
2026-04-02 21:50:32.1775166632
Is substitution a good strategy when I have to integrate a natural log?
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To solve $$\int\ln(u) \,du$$ a common trick is to treat the integral as $$\int 1 \cdot \ln(u) \, du$$ and use integration by part. So $$\int 1 \cdot \ln(u) \, du = u \ln(u)+\int 1\cdot \,du = u\ln(u)+u +C. $$