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int(1)^(e)(dx)/(x(1+logx))...

`int_(1)^(e)(dx)/(x(1+logx))`

Text Solution

Verified by Experts

The correct Answer is:
`log2`
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int_(1)^(2)(dx)/(x(1+logx)^(2))

If I_(1)=int_(e )^(e^(2)) (dx)/(log x) and I_(2)= int_(1)^(2)(e^(x))/(x)dx , then which of the following is correct ?

int_(1)^(e)(1+logx)/(x)dx

int_(1)^(e)(logx)^(2)dx

int_(0)^(1)e^(-x)dx

int_(0)^(1)2e^(x)dx

Prove that, int_(2)^(e)[(1)/(logx)-(1)/((logx)^(2))]dx=e-(2)/(log2)

The value of int_(0)^(1)(x^(a)-1)/(logx)dx is

int_(0)^(1)(dx)/(e^(x)+e^(-x))

int_(0)^(1)(dx)/(e^(x)+e^(-x))