Integration with Partial Fractions

Find the partial fraction decomposition of the rational function: (3x + 2) / (x^2 + 5x + 6)

• (1/(x + 2)) + (2/(x + 4))

• (1/(x + 3)) + (2/(x + 4))

• (1/(x + 2)) + (2/(x + 5))

• (1/(x + 2)) + (2/(x + 3))

Solve the following integral using partial fractions: ∫ (4x + 3) / (x^2 + 4x + 3) dx

• ln|x + 1| + 3ln|x + 2| + C

• ln|x + 2| + 3ln|x + 3| + C

• ln|x + 1| + 3ln|x + 3| + D

• ln|x + 1| + 3ln|x + 3| + C

Express the rational function (2x^2 + 5x + 3) / (x^3 + 3x^2 + 2x) as a sum of partial fractions

• (1/x) + (2/(x+1)) - (1/(x+2))

• (1/x) + (2/(x+1)) + (1/(x+2))

• (1/x) - (2/(x+1)) - (1/(x+2))

• (1/x) - (2/(x+1)) + (1/(x+2))

Evaluate the integral ∫ (x^2 + 3x + 2) / (x^3 + 4x^2 + 4x) dx using partial fractions

• A ln|x| + B ln|x+2| + C/(x+2) + D

• A ln|x| + B ln|x+2| - C/(x+2) + D

• A ln|x| + B ln|x+2| - C/(x+2)

• A ln|x| + B ln|x+2| + C/(x+2)

Find the partial fraction decomposition of the rational function: (5x^2 + 7x + 2) / (x^2 + 6x + 8)

• (1/(x + 4)) + (4/(x + 2))

• (1/(x + 4)) + (4/(x + 2)) + (3/(x + 3))

• (1/(x + 4)) + (4/(x + 2)) + (2/(x + 1))

• (1/(x + 4)) + (4/(x + 2)) + (5/(x + 5))

Solve the following integral using partial fractions: ∫ (3x + 1) / (x^2 + 2x + 1) dx

• 3ln|x + 1| + 2/(x + 1) + D

• 3ln|x + 1| + 2/(x - 1) + C

• 3ln|x + 1| + 2/(x + 1) + C

• 3ln|x + 1| + 2/(x - 1) + D

Express the rational function (x^3 + 2x^2 + x) / (x^2 + 3x + 2) as a sum of partial fractions

• (1/(x + 2)) + (1/(x + 3))

• (1/(x + 1)) + (1/(x + 3))

• (1/(x + 1)) + (1/(x + 2))

• (1/(x + 1)) + (-1/(x + 2))

Evaluate the integral ∫ (2x^2 + 5x + 3) / (x^3 + 2x^2 + x) dx using partial fractions

• A ln|x| + B ln|x+1| + C/(x^2 + 1)

• A ln|x| + B ln|x+1| + C/(x^3 + 2x^2 + x)

• A ln|x| + B ln|x+1| + C/(x+1)

• A ln|x| + B ln|x+1| - C/(x+1)

Find the partial fraction decomposition of the rational function: (4x^2 + 9x + 5) / (x^2 + 4x + 4)

• (1/(x + 2)) + (2/(x + 2))

• (1/(x + 2)) + (2/(x + 2)^3)

• (1/(x + 2)) + (2/(x + 2)^4)

• (1/(x + 2)) + (2/(x + 2)^2)

Solve the following integral using partial fractions: ∫ (2x + 3) / (x^2 + 3x + 2) dx

• ln|x - 1| + ln|x + 2| + C

• ln|x - 1| + ln|x - 2| + C

• ln|x + 1| + ln|x + 2| + C

• ln|x + 1| + ln|x - 2| + C