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Integration

15 / x[In(x)]^4  dx 
 
Ans: -5 / [In(x)]^3 + C
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2 Answers

I am very sorry. Please accept my apologies. I completely misread the problem. I had the x term in the denominator to the power 4 as well. That makes the whole thing much more complicated. Upon further research, that integral would boil down to a special function E(t) = integral ( e^(-x)/x) That's two misreadings in one day. Time out.

∫15 / x[In(x)]dx = ?
 
Try a change of variable.
 
Let u(x) = ln(x).
 
du = dx/x ⇒ dx = x du
 
Then
 
∫15 / x[In(x)]4 dx = 15 ∫x du / (xu4) = 15 ∫du/u4 = 15 ∫u-4 du = 15u-3/(-3) + C
 
∫15 / x[In(x)]4 dx = -5/u3 + C = -5/[ln(x)]3 + C