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Use limits of definite integrals to calculate each of the improper integrals in Exercises.

1x+1x2dx

Short Answer

Expert verified

The improper integral 1x+1x2dxdiverges.

Step by step solution

01

Step 1. Given information. 

The given integral is the following.

1x+1x2dx

02

Step 2. Value of integral. 

Consider functionf(x)=x+1x2

localid="1648879879677" f(x)=x+1x2=xx2+1x2=1x+1x21x+1x2>1x2

In the interval [1,)we have localid="1648879786507" x+1x2>1x2.

As we know that localid="1648884171467" 11x2dxis converse and integral of functions less than 1x2will be converse.

But x+1x21x2so it cannot be converse.

so1x+1x2is diverse.

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