Solve the Integral of (2x+3)/(x^2+4x+3) with Substitution

Math Problem Statement

Найти интеграл ∫(2x+3)/(x^2+4x+3) dx. Шаг 1: Сделайте замену переменной

This integral requires a substitution to simplify the calculation. Here's the integral:

$\int \frac{2x + 3}{x^2 + 4x + 3} \, dx$

Factor the denominator: $x^2 + 4x + 3 = (x + 1)(x + 3)$

So the integral becomes: $\int \frac{2x + 3}{(x + 1)(x + 3)} \, dx$

We can split the fraction using partial fraction decomposition or proceed with substitution. Which method would you like to see explained?

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Integral Calculus
Substitution Method
Partial Fraction Decomposition

Integral of a rational function
Factorization of quadratic expressions: ax^2 + bx + c = (x + m)(x + n)
Basic integration rules

Fundamental Theorem of Calculus

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