Evaluate the following integral:
$integral subscript 1 superscript 2 fraction numerator 5 straight x squared over denominator straight x squared plus 4 straight x plus 3 end fraction dx$

Solution

Let I = $integral subscript 1 superscript 2 fraction numerator 5 straight x squared over denominator straight x squared plus 4 straight x plus 3 end fraction dx space equals space 5 integral subscript 1 superscript 2 fraction numerator straight x squared over denominator left parenthesis straight x plus 1 right parenthesis space left parenthesis straight x plus 3 right parenthesis end fraction dx$
$equals space 5 integral subscript 1 superscript 2 open square brackets 1 plus fraction numerator left parenthesis negative 1 right parenthesis squared over denominator left parenthesis straight x plus 1 right parenthesis space left parenthesis negative 1 plus 3 right parenthesis end fraction plus fraction numerator left parenthesis negative 3 right parenthesis squared over denominator left parenthesis negative 3 plus 1 right parenthesis space left parenthesis straight x plus 3 right parenthesis end fraction close square brackets dx equals space 5 integral subscript 1 superscript 2 open square brackets 1 plus fraction numerator 1 over denominator 2 left parenthesis straight x plus 1 right parenthesis end fraction minus fraction numerator 9 over denominator 2 left parenthesis straight x plus 3 right parenthesis end fraction close square brackets dx equals space 5 open square brackets straight x plus 1 half log left parenthesis straight x plus 1 right parenthesis minus 9 over 2 log left parenthesis straight x plus 3 right parenthesis close square brackets subscript 1 superscript 2$
$equals space 5 space open square brackets straight x plus 1 half log left parenthesis straight x plus 1 right parenthesis minus 9 over 2 log left parenthesis straight x plus 3 right parenthesis close square brackets subscript 1 superscript 2 equals space 5 open square brackets open parentheses 2 plus 1 half log 3 minus 9 over 2 log 5 close parentheses space minus space open parentheses 1 plus 1 half log 2 minus 9 over 2 log 4 close parentheses close square brackets equals space 5 open square brackets 1 plus 1 half log 3 minus 9 over 2 log 5 minus 1 half log 2 plus 9 over 2 log 4 close square brackets equals space 5 open square brackets 1 plus 1 half left parenthesis log 3 minus log 2 right parenthesis minus 9 over 2 left parenthesis log space 5 space minus log space 4 right parenthesis close square brackets equals space 5 open square brackets 1 plus 1 half log open parentheses 3 over 2 close parentheses minus 9 over 2 log open parentheses 5 over 4 close parentheses close square brackets$

For Daily Free Study Material Join wiredfaculty

Integrals

Evaluate the following integral:
$integral subscript 1 superscript 2 fraction numerator 5 straight x squared over denominator straight x squared plus 4 straight x plus 3 end fraction dx$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction