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Select Expressions Matching the Value Indefinite Integral Int X^2(1-2x+x^2)dx (x^3(6x^2-15x+10))/(30)+C

Вопрос

Select all expressions matching the value of indefinite integral int x^2(1-2x+x^2)dx (x^3(6x^2-15x+10))/(30)+C (x^3)/(3)(-x^2+(x^3)/(3))+C -(x^4)/(2)+(x^5)/(5)+C

Решения

4.5 (166 Голоса)
Лидия
Экспертная проверка
профессионал · Репетитор 6 лет

Ответ

To determine which expressions match the value of the indefinite integral , we need to evaluate the integral.First, let's simplify the integrand: Now, we can integrate term by term: Integrating each term separately: Putting it all together: Now, let's compare this result with the given options:1. : Simplifying this expression: This expression does not match the result we obtained.2. : Simplifying this expression: This expression does not match the result we obtained.3. : This expression matches the result we obtained.Therefore, the correct answer is: