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

Step-by-step Solution

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Final answer to the problem

The integral diverges.

Step-by-step Solution

How should I solve this problem?

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  • 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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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.

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

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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.

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Function Plot

Plotting: $\frac{1}{1+x^3}$

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