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Find the values of $ p $ for which the integral converges and evaluate the integral for those values of $ p $.

$ \displaystyle \int_0^1 x^p \ln x\ dx $

the integral converges to $-\frac{1}{(p+1)^{2}}$ if $p>-1$ and diverges otherwise

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Missouri State University

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