Partial fractions

41 practice questionsIntegral CalculusStep-by-step solutions

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Identify the correct factorization of the denominator $x^2-16$ into its prime (linear) factors

(x+4)(x-4)

(x-4)(x-4)

(x+3)(x+3)

(x+2)(x-2)

E.None

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Find $\int \dfrac{3x^2}{(x-1)(x^2+x+1)}\,dx$ .

\ln(x^3-1)+C

\ln(x^3+1)+C

3\ln(x-1)+C

\ln(x-1)+\ln(x^2+x+1)-C

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When the denominator of a rational function has an irreducible quadratic factor $(x^2+bx+c)$ with no real roots, the corresponding partial-fraction numerator should be taken as

A.a general linear term

Ax+B

B.a single constant

A

C.a term

A x^2

D.the same form as for a repeated linear factor,

\frac{A}{x-r}+\frac{B}{(x-r)^2}

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Partial fractions

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