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# Integrate the function $\frac{1}{1+x^3}$ from $1$ to $\infty$

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##  Final answer to the problem

The integral diverges.

##  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
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1

Rewrite the expression $\frac{1}{1+x^3}$ inside the integral in factored form

$\int\frac{1}{\left(x+1\right)\left(x^2-x+1\right)}dx$

Learn how to solve problems step by step online.

$\int\frac{1}{\left(x+1\right)\left(x^2-x+1\right)}dx$

Learn how to solve problems step by step online. Integrate the function 1/(1+x^3) from 1 to infinity. Rewrite the expression \frac{1}{1+x^3} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x+1\right)\left(x^2-x+1\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 \left(x+1\right)\left(x^2-x+1\right). Multiplying polynomials.

##  Final answer to the problem

The integral diverges.

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more