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Integrate the functions.$$\frac{1}{x(\log x)^{m}}, x>0, m \neq 1$$
01:25
Suman Saurav T.
Calculus 2 / BC
Chapter 7
Integrals
Section 2
Integration as an Inverse Process of Differentiation
Integration Techniques
Missouri State University
Campbell University
University of Nottingham
Boston College
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in this question we are required to find in detail of one divided by thanks log x rays to the fire and yeah, X is greater than zero and mm is not equal to what. So let us start with the simplification. We first of all right integral off one divided by X log x rays to the bar. M be it. Now we made the substitution log X equal to T. Taking differential on both the sides. We get when by X. The X is equal to D. T. Substituting both the values back in 19 grill we get integral off one by X. D X S. V. T divided by Now get 16. So we get to the bottom. Now this can be read in us. Interior lofty raised the par minus in DT and since M is not equal to one, the integral will be periods. The par minus M plus one divided by minus M plus one plus the constant of integration. Capital C. We can now substitute the value of T back in the expression to get log x rays to the par minus M plus one Divided by -M-plus one plus captaincy
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