Answer to Question #147643 in Algebra for liam donohue

Question

Find the most general antiderivative for the function 6x−−√3−5x2−−√3.
Antiderivative =

Answer 1

Mathematically, anti-derivative function is given by; ∫xⁿ= (xⁿ⁺¹)/ (n+1) (+C)

Therefore, we proceed to calculate the antiderivative of 6x−−√3−5x²−−√3

First of all, we simplify our equation as follows;

(6x)--(√3)−(5x²)--(√3) = 6x + √3 - 5x² + √3 = 6x + (√3 + √3) - 5x² = 6x + 2√3 - 5x² = -5x² + 6x + 2√3.

we then procced to integrate function -5x² + 6x + 2√3.

(-5x²⁺¹/2+1) + (6x¹⁺¹/1+1) + (2√3x⁰⁺¹/0+1) + C

(-5x³/3) + (6x²/2) + (2√3x¹/1) + C= (-5/3)x³ + (6/2)x² + (2√3x¹/1) + C

therefore, the general antiderivative = (-5/3)x³ + 3x² + 2√3x + C.