Вычислить неопределенный интеграл. Created by Filka7. algebra-ru

Интегрирование степенной функции:Находим интеграл:

Вычислить неопределенный интеграл...

Filka7 @Filka7

December 2021 1 16 Report

Вычислить неопределенный интеграл

Answers & Comments

Artem112

Verified answer

Интегрирование степенной функции:

$\int x^adx=\dfrac{x^{a+1}}{a+1}+C,\ a\neq -1$

Находим интеграл:

$\int\left(\sqrt{x}-2x^3+6\right)x^2dx =\int\left(x^{\frac{1}{2} }-2x^3+6\right)x^2dx =\int\left(x^{\frac{5}{2} }-2x^5+6x^2\right)dx =$

$=\dfrac{x^{\frac{5}{2} +1}}{\frac{5}{2} +1} -\dfrac{2x^6}{6} +\dfrac{6x^3}{3}+C =\dfrac{x^{\frac{7}{2} }}{\frac{7}{2} } -\dfrac{x^6}{3} +2x^3+C=\boxed{ \dfrac{2}{7}x^3\sqrt{x}-\dfrac{x^6}{3} +2x^3+C}$

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Verified answer

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