Question

If the integral of the quantity 4 times x minus 2 and the product of the quantity x and the quantity x plus 1 dx = (A)Ln|x| + (B)Ln|x + 1| + constant, then what is the value of A - B? (5 points)

-8
-4
4
8

Answer 1

-8

Explanation:

f(x) = (4x − 2) / (x (x + 1))

Write f(x) as the sum of two fractions.

f(x) = A / x + B / (x + 1)

Combine back into one fraction using the least common denominator.

f(x) = (A (x + 1) + Bx) / (x (x + 1))

f(x) = ((A + B) x + A) / (x (x + 1))

This equals the original numerator of 4x − 2, so match the coefficients.

A + B = 4

A = -2

Solving for B, B = 6.

Therefore, A − B = -2 − 6 = -8.

Answer 2

i think 8

Explanation: