Intergration

Question

integrate (4-x²)(3+x) / 2x⁵

Answer 1

∫[(4-x²)(3+x)/(2x⁵)]dx

 

            = ∫[(-3x²+4x-x³+12)/(2x⁵)]dx  (divide each term of the                                                                 numerator by the denominator)

 

            = ∫[ (-3/2)x^-3 +2x^-4 - (1/2)x^-2 + 6x^-5]dx

 

            = (-3/2)(-1/2)x^-2 + 2(-1/3)x^-3 - (1/2)(-1)x^-1 + 6(-1/4)x^-4 + C

 

            = 3/(4x²) - 2/(3x³) + 1/(2x) - 3/(2x⁴) + C