Evaluate:

Question

Question

Answer 1

Concept:

Partial Fraction:

Factors in the denominator	Corresponding Partial Fraction
(x - a)
(x – b)2
(x - a) (x – b)
(x – c)3
(x – a) (x2 – a)
(ax2 + bx + c)

Calculation:

Here we have to find the value of

Let e^x = t and by differentiating ex = t with respect to x we get

⇒ e^x dx = dt or dx = dt/e^x = dt/t

Let

⇒ 1 = A (t - 1) + B t ---------(1)

By putting t = 0 on both the sides of (1) we get A = - 1

By putting t = 1 on both the sides of (1) we get B = 1

As we know that where C is a constant

By substituting ex = t in the above equation we get