Question

integral(4/x^2+5x+6) I've done this much for now, but now I'm confused again.

 

 

Answer 1

Step 1 :

Find .

First factorize the denominator of the integrand.

Find the partial fractions of the integrand by using partial fraction decomposition.

Step 2 :

The integrand is .

Equate the coefficients of x  terms.

       (1)

Equate the constant terms.

   (2)

Multiply equation (1) by 2, then subtract the equation from equation (2).

Substitute in equation (1).

Substitute the values and in .

The integrand is .

Step 3 :

Then the integral is,

Apply formula : .

Thus, .

Solution :

.