College Calculus 2

Question

Find the most general antiderivative.

 

f(x) = (x^5-x^3+8x)/x^4

Answer 1

∫[(x⁵ - x³ + 8x) / x⁴)]dx

 

Divide each term of the numerator by the denominator and simplify:

 

    ∫(x - 1/x + 8/x³)dx = ∫xdx - ∫(1/x)dx + 8∫x^-3dx

 

                                 = (1/2)x² - ln l x l + 8(x^-2/(-2)) + C

 

                                 = (1/2)x² - ln l x l - 4/x² + C