Question

X4+1
11. (a) Evaluate: integration x²-1/(x-1)² (x+3)

(b) Evaluate : integration root (36x²-25) dx
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Answer 1

Step-by-step explanation:

11.a.

$\int \frac{ {x}^{2} - 1}{(x - 1) ^{2}(x +3 ) } dx$

$= \int \frac{(x + 1)}{(x - 1)(x + 3)} dx$

$= \int \frac{dx}{2(x - 1)} + \int \frac{dx}{2(x + 3)}$

$= \frac{1}{2} ln(x - 1) + \frac{1}{2} ln(x + 3) + c$

$= ln((x - 1)^{ \frac{1}{2} } ) + ln((x + 3)^{ \frac{1}{2} } ) + c$

$= ln( \sqrt{(x - 1)(x + 3)} ) + c$