Answer :

Let

Firstly, we rewrite the linear term as the 1st derivative of (5 + 4x – 2x2) i.e.






On comparing the coefficients of x and the constant term, we get


-4A = 3



and 4A + B = 5



-3 + B = 5


B = 8



So,




Let I = I1 + I2 …(i)


For I1,


Let 5 + 4x – 2x2 = t


Taking derivatives of both the sides, we get


(4 – 4x)dx = dt



For I2,






{Here, we add and subtract 2 to make the (a – b)2}





Now, let


Taking the derivative of both the sides, we get




So,




Now, we use the standard integral formula




Now, put back the value of t, we get








Put the value of I1 and I2 in eq. (i)



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