# A roaring paper tiger (My sixth integral problem)

**Calculus**Level 5

\[ \displaystyle \int_{-1}^{1} \sqrt[3]{x^3 + 3x^2 + \sqrt[3]{27x^3 + 27x^2 + \sqrt[3]{729x^3 + 243x^2 +\sqrt[3]{19683x^3 + 2182 x^2 +\cdots} }}}dx \]

Evaluate the integral above.

**Clarification:**

The coefficient of \(x^3 \) is given by \(3^{3n-3} \), where \(n\) is a positive integer.

The coefficient of \(x^2 \) is given by \(3^{2n-1} \), where \(n\) is a positive integer.