Q. 45.0( 1 Vote )

Evaluate the foll

Let

Let us assume

We know and derivative of a constant is 0.

x + 2 = λ(2x2-1 + 1 + 0) + μ

x + 2 = λ(2x + 1) + μ

x + 2 = 2λx + λ + μ

Comparing the coefficient of x on both sides, we get

2λ = 1

Comparing the constant on both sides, we get

λ + μ = 2

Hence, we have

Substituting this value in I, we can write the integral as

Let

Now, put x2 + x + 1 = t

(2x + 1)dx = dt (Differentiating both sides)

Substituting this value in I1, we can write

Recall

Let

We can write

Hence, we can write I2 as

Recall

Substituting I1 and I2 in I, we get

Thus,

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