Determine the value of ( _ 0 ^ 2 2x^ 3 -3x^ 2 +x+5 x^ 2 +1 ,dx ).

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

Determine the value of ∫022x3−3x2+x+5x2+1 dx\displaystyle \int_{0}^{2} \frac{2x^{3}-3x^{2}+x+5}{x^{2}+1}\,dx. (a) −2+12ln⁡5+8arctan⁡2-2+\dfrac{1}{2}\ln 5+8\arctan 2 (b) −2−12ln⁡5+4arctan⁡2-2-\dfrac{1}{2}\ln 5+4\arctan 2 (c) −2−12ln⁡5+8arctan⁡2-2-\dfrac{1}{2}\ln 5+8\arctan 2 (d) −2−12ln⁡5+8ln⁡2-2-\dfrac{1}{2}\ln 5+8\ln 2

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