10 from 10 Solve the definite integral and enter your answer in decimal format (use the a/b form for irrational fractions) int _(-1)^1((2x)/(3)+(3)/(x^4))dx square

To solve the definite integral \(\int_{-1}^{1} \left( \frac{2x}{3} + \frac{3}{x^4} \right) \, dx\), we need to evaluate each term separately.First, let's consider the integral of the first term: Since is an odd function (i.e., \(f(-x) = -f(x)\)), the integral of an odd function over a symmetric interval around zero is zero: Next, let's consider the integral of the second term: Similarly, is also an odd function. Therefore, its integral over the interval is also zero: Since both integrals are zero, the value of the original definite integral is: Thus, the answer is: