Answer:

i think it is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

I = ∫2x/x²+3x+2 . dx

I can help you with that integral.

First, we can factor the denominator of the integrand as follows:

x² + 3x + 2 = (x + 2)(x + 1)

Then, we can rewrite the integrand as:

2x / (x + 2)(x + 1)

We can then use partial fraction decomposition to rewrite the integrand as:

A / (x + 2) + B / (x + 1)

where A and B are constants that we need to solve for.

Multiplying both sides by (x + 2)(x + 1), we get:

2x = A(x + 1) + B(x + 2)

Expanding and equating coefficients of x on both sides, we get:

2 = A + B

Equating constant terms on both sides, we get:

0 = A + 2B

Solving these equations simultaneously, we get:

A = -2 and B = 4

Therefore, the integral becomes:

∫ [ -2 / (x+2) ] dx + ∫ [ 4 / (x+1) ] dx

Integrating each term separately, we get:

-2 ln|x+2| + 4 ln|x+1| + C

where C is the constant of integration.

So the final answer is:

-2 ln|x+2| + 4 ln|x+1| + C