Since the degree of the numerator is less than the degree of the denominator, we don't need to divide. We factor the denominator as

As given,

I =

Since the degree of the numerator is less than the degree of the denominator, we don't need to divide.

We factor the denominator as x(x-2)

The partial fraction decomposition is

we get

3x = A(x-2) + B(x)

⇒3x = x(A+B) - 2A

By comparing , we get

A+ B = 3 , -2A = 0

⇒A = 0 and B = 3- A = 3-0 = 3

∴ we get

A = 0, B = 3

Therefore, the integral become

4th option is correct xy=-10

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answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation: