this one question ### Calculus: Indefinite Integrals#### Find the following indefinite integrals:(a) \[\int x^{-4} \sec^2(x^{-3} + 1) \sqrt[3]{\tan(x^{-3} + 1)} \, dx\]In this problem, we aim to determine the indefinite integral of the given function involving trigonometric functions, secant and tangent, as well as power functions and a cube root.1. **Expression Breakdown**: - \( x^{-4} \): denotes a variable \(x\) raised to the power of \(-4\). - \( \sec^2(x^{-3} + 1) \): secant squared function with its argument being \(x^{-3} + 1\). - \( \tan(x^{-3} + 1) \): tangent function with the same argument as the secant function. - \( \sqrt[3]{\tan(x^{-3} + 1)} \): cube root of the tangent function.2. **Integral Notation**: - \(\int\): indicates the integral of the function that follows. - \( dx \): indicates the variable of integration.### Steps to ApproachTo solve such integrals, one might consider the use of substitution methods, integration by parts, or recognizing a common integral form.Please proceed to solve the integral by applying appropriate calculus techniques as per your curriculum guidelines.

Name: this one question ### Calculus: Indefinite Integrals#### Find the foll
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: this one question ### Calculus: Indefinite Integrals#### Find the following indefinite integrals:(a) \[\int x^{-4} \sec^2(x^{-3} + 1) \sqrt[3]{\tan(x^{-3} + 1)} \, dx\]In this problem, we aim to determine the indefinite integral of the given function