Which of the following integrals must first be rewritten by dividing the polynomials…

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Which of the following integrals must first be rewritten by dividing the polynomials so that the degree of the numerator is less than that of the denominator? (a) ∫2xx2+1 dx\displaystyle \int \frac{2x}{x^{2}+1}\,dx (b) ∫x3+2x+1x2−1 dx\displaystyle \int \frac{x^{3}+2x+1}{x^{2}-1}\,dx (c) ∫x2+3x3+1 dx\displaystyle \int \frac{x^{2}+3}{x^{3}+1}\,dx (d) ∫x+1x2+4 dx\displaystyle \int \frac{x+1}{x^{2}+4}\,dx

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