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Find Integral(E^X Dx)By((E^X - 1)Square2 (Ex + 2))` - CBSE (Science) Class 12 - Mathematics

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Question

Find `int(e^x dx)/((e^x - 1)^2 (e^x + 2))`

Solution

`int(e^x dx)/((e^x - 1)^2 (e^x + 2))`

Putting ex = t and exdx = dt, we get

`int(e^x dx)/((e^x - 1)^2 (e^x + 2)) = int (dt)/((t-1)^2(t+2))`

Using partial fraction, we have

`1/((t-1)^2 (t + 1)) = A/(t-1)^2 +  B/(t -1) + C/(t +2)`

⇒ 1 = A(t+2) + B(t−1)(t+2) + C(t−1)2 .....(1)

Putting t = 1 in (1), we get

`A = 1/3`

Putting t = −2 in (1), we get

C = `1/9`

Comparing the coefficients of t2 on both sides of (1), we get

0

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Solution Find Integral(E^X Dx)By((E^X - 1)Square2 (Ex + 2))` Concept: Methods of Integration - Integration Using Partial Fractions.
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