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If F(x) = int(x^(2))^(x^(3))(1)/(lnt) dt...

If `F(x) = int_(x^(2))^(x^(3))(1)/(lnt) dt` then find `F'(e )`

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`F'(x) = (3x^(2))/(lnx^(3)) - (2x)/(lnx^(2)) = (x^(2))/(lnx)-(x)/(lnx)= (x(x-1))/(lnx)` now `F'(e) = (e(e-1))/(lne) = e(e-1)`
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
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  4. Let alpha & beta be distinct positive roots of the equation tanx = 2x,...

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  15. If n gt 1. Evaluate int(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

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  19. Given that lim(x to oo)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1...

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