RESOLUÇÃO DA INTEGRAL DE [ x + √(x² + 1 ) NO ITERVALO DE 0 A √3

Solve the integral of [ x + √(x² + 1 ) ] , in the interval from 0 to √3, and select the correct alternative. a) √3 ln ( √3 + 2 ) - 1 Error due to confusing the integrand with arcsin(x) b) 3/2 + √3 + 1/2 ln ( √3 + 2 ) Correct c) 3/2 + √3 + ln ( √3 + 2 ) Forgetting the factor 1/2 in the logarithmic term d) 3/2 + 1/2 ln ( √3 + 2 ) Omission of the algebraic term resulting from the integral of √(x² + 1 ) e) 3/2 + √3 Complete disregard of the logarithmic term Due to the fact that the question is from a "high school" exam, I would recommend avoiding the hyperbolic "universe". The question under analysis is didactically rich, as it allows the student to apply fundamental calculus concepts. This question covered integrals, linearity of the integral, trigonometric or hyperbolic substitutions, and integration by parts. This question was based on a proposed change of answer choices, as described above.