   Chapter 7.R, Problem 49E

Chapter
Section
Textbook Problem

# Evaluate the integral or show that it is divergent. ∫ − ∞ ∞ d x 4 x 2 + 4 x + 5

To determine

To Find:dx4x2+4x+5

Explanation

Formula Used:1(x+a)2+b2=1btan1(x+ab)+C

Calculation:

Here the integral is improper but it has no point of discontinuity on (,). Because the denominator has no real roots. So,

14x2+4x+5dx=a14x2+4x+5dx+a14x2+4x+5dx=limλλa14x2+4x+5dx+limtat14x2+4x+5dx=14limλλa1(x+12)2+1dx+14limtat1(x+12)2+1dx

Now, use the formula mentioned above to find the integral

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