Math Problem Statement

QUESTION 3 (35 MARKS) Integrate the following equations i. / (lx 5 — x 3 + x ) dx

Solution

It looks like the equation you provided is not fully clear. Could you confirm or clarify it for me?

From the given part, it seems like you want to integrate something like:

(l(x)5x3+x)dx\int \left( \frac{l(x)}{5} - x^3 + x \right) \, dx

But the part l(x) seems like a potential typo or abbreviation for a function. If it's referring to a logarithmic function, it might be:

(ln(x)5x3+x)dx\int \left( \frac{\ln(x)}{5} - x^3 + x \right) \, dx

Please confirm or clarify the expression, and I can help you with the integration.

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Math Problem Analysis

Mathematical Concepts

Integration
Indefinite Integrals
Logarithmic Functions
Polynomial Functions

Formulas

∫ x^n dx = (x^(n+1)) / (n+1) + C (for n ≠ -1)
∫ ln(x) dx = x ln(x) - x + C
∫ a dx = ax + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Undergraduate Calculus / Advanced High School