Q19 of 26 Page 1

Evaluate:

Let


3x + 1 = A(-2 – 2x) + B


3x + 1 = -2A – 2Ax + B


On comparing


-2Ax = 3x



and -2A + B = 1



⇒ 3 + B = 1


⇒ B = 1 – 3


⇒ B = -2



…(A)


Solving …(i)


Let 5 – 2x – x2 = t


Differentiating with respect to x, we get




⇒ (-2 – 2x) dx = dt


Putting the value of (-2 – 2x)dx in eq. (i), we get







= -3√t + C1


…(ii)






Let y = x + 1


⇒ dy = dx




We know that,




Replacing y by x + 1


…(iii)


Putting the value (ii) and (iii) in eq. (A)





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