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# Tag Archives: Integral

## Definite logarithmic integral

Let . Evaluate the integral:

**Solution**

We have successively:

## Definite parametric integral

Let . Evaluate the integral

**Solution**

The key substitution is . Applying it we see that

Thus,

Thus , .

## Definite integral

Let be a function such that

Evaluate the integral .

**Solution**

We multiply the given equation by . Thus,

Let and .

We now deal with the first integral:

As for the second integral we have:

Hence,

## Offset logarithmic integral inequality

Prove that

**Solution**

We have successively:

## A Riemann sum II

Evaluate the limit:

**Solution**

We have successively: