Evaluate the definite integral K= _ 0 ^ 1 2x^ 2 +3x+1 (x+1)(x^ 2 +1) ,dx

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Evaluate the definite integral

K=\int_{0}^{1} \frac{2x^{2}+3x+1}{(x+1)(x^{2}+1)}\,dx.

(a) Decompose the integrand into partial fractions with denominators

x+1

and

x^{2}+1

. (b) Hence determine the exact value of

K

, simplifying your result as far as possible.