найти неопределенный интеграл2) (4x³ + 5x⁴ + 6x⁵)dx; 3) (cosx

July 2022 2 29 Report

найти неопределенный интеграл
2) (4x³ + 5x⁴ + 6x⁵)dx;

3) (cosx - 2)dx;

4) (3 + sinx)dx.

Matematiktm

Ответ:

$\displaystyle \int (4x^3+5x^4+6x^5)\, dx=x^4+x^5+x^6+C\\\\\\\int (cosx-2)\, dx=sinx-2x+C\\\\\\\int (3+sinx)\, dx=3x-cosx+C$

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Verified answer

Ответ:

$\int\limits^._. {(4x^{3} + 5x^{4} + 6x^{5} )} \ dx =4\int\limits^._. {x^{3}} \ dx + 5\int\limits^._. {x^{4}} \ dx + 6\int\limits^._. {x^{5} } \ dx =4*\frac{x^{4} }{4} +5*\frac{x^{5} }{5} +6*\frac{x^{6} }{6} =x^{4} +x^{5} +x^{6}+C$

Объяснение:

$\int\limits^._. {(cosx - 2)} \, dx =\int\limits^._. {cosx } \, dx -2\int\limits^._. {} \, dx =sinx-2x+C$

$\int\limits^._. {(3 + sinx)} \, dx =3x-cosx+C$

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