Find the general antiderivative of 𝑓(𝑥)=23𝑥^−3/5 and check the answer by differentiating.

Question

(Use symbolic notation and fractions where needed. Use 𝐶 for the arbitrary constant. Absorb into 𝐶 as muсh as possible.)

∫ 𝑓(𝑥) 𝑑𝑥 =

Answer 1

∫f(x)dx = 23 ∫x^-3/5dx +C = 23(5/2)x^2/5 + C. Taking the derivative of the new function gives 23(5/2)(2/5)x^-3/5 which comes about by reducing the exponent by1.