Vault Of Euclid

Integral of a Rational Function using Partial Fractions

Techniques of integration core

\(\int \frac{x^2+2}{x(x^2+5x+6)} \, dx\)

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What you need first

Factoring quadratic polynomials
Solving linear equations
The integral of 1/x

What this problem tests

Tests the ability to factor a polynomial, set up and solve a partial fraction decomposition with distinct linear factors, and integrate the result.

This is a standard problem in a Calculus II course covering techniques of integration.

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Reduction Formula for a Rational Function core
Area Under the Curve of ln(x)/x warmup

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