Q. 143.8( 42 Votes )

Evaluate <span la

Answer :

Let I =

Multiplying by 5 in numerator and denominator


I =


I =


I = I1 + I2


I1 =


Let 5x2 + 1 = t ….(i)


d(5x2 + 1) = dt


10x dx = dt …..(ii)


When x = 0; t = 5 × 02 + 1 = 1


When x = 1; t = 5 × 12 + 1 = 6


Substituting (i) and (ii) in I1


I1 = []


I1 =


I1 =


I2 = []


I2 =


I2 = 3/√5 tan-15


I = I1 + I2


I = 1/5 log 6 + 3/√5 tan-15


= 1/5 log 6 + 3/√5 tan-15


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