Ответ:
[tex]\boxed{ \displaystyle \boldsymbol{ \int {x^{2} (1 + 3x)} \, dx = \frac{x^{3}}{3} + \frac{3x^{4}}{4} + C} }[/tex]
[tex]\boxed{ \displaystyle \boldsymbol{ \int {\frac{22 \cdot dx}{\cos^{2} x} } = 22 \ \rm{ tg} \ x + C}}[/tex]
Примечание:
По таблице интегралов:
[tex]\boxed{\displaystyle \int x^{n} \ dx = \frac{x^{n + 1}}{n + 1};n \neq -1;x > 0 }[/tex]
[tex]\boxed{\displaystyle \int \frac{dx}{\cos^{2} x} = \rm tg \ x + C }[/tex]
Пошаговое объяснение:
[tex]\displaystyle \int {x^{2} (1 + 3x)} \, dx = \int {(x^{2} + 3x^{3})} \, dx = \frac{x^{3}}{3} + \frac{3x^{4}}{4} + C[/tex]
[tex]\displaystyle \int {\frac{22 \cdot dx}{\cos^{2} x} } = 22 \int {\frac{ dx}{\cos^{2} x} } = 22 \ \rm{ tg} \ x + C[/tex]
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Answers & Comments
Ответ:
[tex]\boxed{ \displaystyle \boldsymbol{ \int {x^{2} (1 + 3x)} \, dx = \frac{x^{3}}{3} + \frac{3x^{4}}{4} + C} }[/tex]
[tex]\boxed{ \displaystyle \boldsymbol{ \int {\frac{22 \cdot dx}{\cos^{2} x} } = 22 \ \rm{ tg} \ x + C}}[/tex]
Примечание:
По таблице интегралов:
[tex]\boxed{\displaystyle \int x^{n} \ dx = \frac{x^{n + 1}}{n + 1};n \neq -1;x > 0 }[/tex]
[tex]\boxed{\displaystyle \int \frac{dx}{\cos^{2} x} = \rm tg \ x + C }[/tex]
Пошаговое объяснение:
[tex]\displaystyle \int {x^{2} (1 + 3x)} \, dx = \int {(x^{2} + 3x^{3})} \, dx = \frac{x^{3}}{3} + \frac{3x^{4}}{4} + C[/tex]
[tex]\displaystyle \int {\frac{22 \cdot dx}{\cos^{2} x} } = 22 \int {\frac{ dx}{\cos^{2} x} } = 22 \ \rm{ tg} \ x + C[/tex]