CBSE Class 11-science Answered

1.integral of dx/2x square-1 2.integral of (2x-7).dx/x square-7x+4

Asked by SWETHA v | 13 May, 2014, 05:51: PM

Expert Answer

$integral fraction numerator d x over denominator 2 x squared minus 1 end fraction U sin g space c o n c e p t space o f space p a r t i a l space f r a c t i o n comma space w e space g e t fraction numerator 1 over denominator 2 x squared minus 1 end fraction equals minus fraction numerator 1 over denominator 2 open parentheses square root of 2 x plus 1 close parentheses end fraction plus fraction numerator 1 over denominator 2 open parentheses square root of 2 x minus 1 close parentheses end fraction N o w comma space integral fraction numerator d x over denominator 2 x squared minus 1 end fraction equals integral open parentheses minus fraction numerator 1 over denominator 2 open parentheses square root of 2 x plus 1 close parentheses end fraction plus fraction numerator 1 over denominator 2 open parentheses square root of 2 x minus 1 close parentheses end fraction close parentheses d x space space space space space space space space space space space space space space space space space equals minus space fraction numerator 1 over denominator 2 square root of 2 end fraction log open parentheses square root of 2 x plus 1 close parentheses plus fraction numerator 1 over denominator 2 square root of 2 end fraction log open parentheses square root of 2 x minus 1 close parentheses space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator 2 square root of 2 end fraction open square brackets log open parentheses fraction numerator square root of 2 x minus 1 over denominator square root of 2 x plus 1 end fraction close parentheses close square brackets plus C$