Ihave an interesting intergral that seems pretty challenging. after attempting to solve it for some time, i've come up empty handed. can you solve this integral?

indefinite integral of:

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Integration

Integration Property [Multiplied Constant]:                                                            

U-Substitution

Sequences

Series

Taylor Polynomials and Approximations

Power Series

Integration of Power Series:

Multivariable Calculus

Gamma Functions

Step-by-step explanation:

*Note:

If we are talking single-variable calculus, then we would have to write this integral as a power series.

If we are talking multi-variable calculus, then we could integrate this and get an "actual" value.

We are given the integral:

We know that the power series for    is:

To find the power series for    , substitute in x = x³:

Simplify it, we have:

Rewrite the original function:

Rewrite the integrand by including the x⁴ in the power series:

Integrating the power series, we have:

Let's set our variables for u-substitution:

u = x⁵ → du = 5x⁴ dx

Use u-substitution on the integral to obtain:

We see that the integral is an incomplete gamma function:

Simplifying it, we have:

Back-substituting u will give us the final result:

answer: it is d

step-by-step explanation: