Question

HELP! интеграл

Answer 1

Ответ: 1/2*ln(3*x²+6*x+7)-1/(2*√3)*arctg[√3*(x+1)/2]+C.

Пошаговое объяснение:

∫(3*x+2)*dx/(3*x²+6*x+7)=1/2*∫(6*x+4)*dx/(3*x²+6*x+7)=1/2*∫(6*x+6-2)*dx/(3*x²+6*x+7)=1/2*∫(6*x+6)*dx/(3*x²+6*x+7)-∫dx/(3*x²+6*x+7)=1/2*∫d(3*x²+6*x+7)/(3*x²+6*x+7)-1/3*∫dx/(x²+2*x+7/3)=1/2*ln(3*x²+6*x+7)-1/3*∫d(x+1)/[(x+1)²+(2/√3)²]=1/2*ln(3*x²+6*x+7)-1/(2*√3)*arctg[√3*(x+1)/2]+C.

Answer 2

Ответ:

$\frac{1}{2}\ln|3x^2+6x+7|-\frac{1}{2\sqrt{3} } \arctan\frac{\sqrt{3}(x+1)}{2} +C,$   C=Const

Пошаговое объяснение:

Решение в приложении

Answer 3

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To calculate an integral, you need to specify the function and the limits of integration. For example, you can write `integral of x^2 from 0 to 1` or `∫_0^1 x^2 dx`. You can use parentheses, brackets, and braces to group expressions. You can also use standard mathematical functions and constants, such as `sin`, `cos`, `exp`, `pi`, etc.

If you want to see the steps of integration, you can write `show steps` after the integral. For example, `integral of sin(x) from 0 to pi show steps`. I will show you the method and the intermediate steps of integration.

If you need more help, you can check out some online resources that explain how to integrate functions using different methods. Here are some links that you can visit:

- [Вычислитель интегралов: находим интегралы с помощью Wolfram|Alpha](https://ru.wolframalpha.com/calculators/integral-calculator) - [Интегралы. Пошаговый калькулятор - MathDF](https://mathdf.com/int/ru/) - [Калькулятор интегралов онлайн](https://ru.onlinemschool.com/math/assistance/integrate/integrate/)

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