Math Problem Statement

integral of x^2-x+6/ x^3 +3x

Solution

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Math Problem Analysis

Mathematical Concepts

Integral Calculus
Algebraic Fractions
Substitution in Integration
Logarithmic and Trigonometric Functions

Formulas

Integral of 1 / (x^2 + a^2) dx = (1/a) * arctan(x/a)
Logarithmic integral: ∫ 1 / u du = ln|u| + C
Substitution Method: u = g(x)

Theorems

Arctangent Integration Theorem
Logarithmic Integration Theorem
Substitution Theorem

Suitable Grade Level

Grades 11-12 (Advanced Calculus)