Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- Load more...
Rewrite the expression $\frac{4x^2+6}{x^3+3x}$ inside the integral in factored form
Rewrite the fraction $\frac{4x^2+6}{x\left(x^2+3\right)}$ in $2$ simpler fractions using partial fraction decomposition
Find the values for the unknown coefficients: $A, B, C$. The first step is to multiply both sides of the equation from the previous step by $x\left(x^2+3\right)$
Multiplying polynomials
Simplifying
Assigning values to $x$ we obtain the following system of equations
Proceed to solve the system of linear equations
Rewrite as a coefficient matrix
Reducing the original matrix to a identity matrix using Gaussian Elimination
The integral of $\frac{4x^2+6}{x\left(x^2+3\right)}$ in decomposed fraction equals
Simplify the expression inside the integral
The integral $\int\frac{2}{x}dx$ results in: $2\ln\left(x\right)$
The integral $2\int\frac{x}{x^2+3}dx$ results in: $-2\ln\left(\frac{\sqrt{3}}{\sqrt{x^2+3}}\right)$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$