D 2.) E /(x-1)⁰ (2x + 3) (x+6)⁰ F
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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