Answer:

To integrate this expression, we can use the method of partial fractions. First, we can write the expression as:

E /(x-1)⁰ (2x + 3) (x+6)⁰ F = A/(x-1) + B/(2x+3) + C/(x+6)

where A, B, and C are constants we need to find. To find them, we can multiply both sides by the common denominator:

E = A(2x+3)(x+6) + B(x-1)(x+6) + C(x-1)(2x+3)

Now we can substitute values of x that will make some of the terms equal to zero. For example, if we substitute x=1, the first term will be zero, so we get:

E = B(1-1)(1+6) + C(1-1)(2\*1+3) = 5C

Similarly, if we substitute x=-3/2, the second term will be zero, so we get:

E = A(2\*(-3/2)+3)(-3/2+6) + C(-3/2-1)(2\*(-3/2)+3) = -21/4A -15/4C

And if we substitute x=-6, the third term will be zero, so we get:

E = A(-6-1)(-6+6) + B(-6-1)(-6+1) = -7A -35B

Now we have three equations and three unknowns, which we can solve to find A, B, and C. Solving for A, we get:

A = (-15/4C - E)/(-21/4)

Solving for B, we get:

B = (-7A - E)/35

And solving for C, we get:

C = E/5

Substituting these values back into our expression, we get:

E /(x-1)⁰ (2x + 3) (x+6)⁰ F = (-15/4C - E)/(-21/4)/(x-1) + (-7A - E)/35/(2x+3) + E/5/(x+6)

Simplifying this expression, we get:

E /(x-1)⁰ (2x + 3) (x+6)⁰ F = (-3/7)/(x-1) + (-1/5)/(2x+3) + (1/5)/(x+6)

Therefore, the integral of E /(x-1)⁰ (2x + 3) (x+6)⁰ F is:

-3/7 ln|x-1| - 1/5 ln|2x+3| + 1/5 ln|x+6| + C

where C is the constant of integration.

Step-by-step explanation:

sorry kung magulo.

Answer:

x=43

Step-by-step explanation:

x-1+2x+3+x+6=180

4x+8=180

4x=180-8

4x=172

x=43