Evaluate : ∫dx/x(x^5+3)

Question

Evaluate : \(\int\frac{dx}{x(x^5+3)}\)

Answer 1

Let I = \(\int\frac{dx}{x(x^5+3)}\)

= \(\int\frac{x^4dx}{x^5(x^5+3)}\)

= \(\frac{1}{5}\)\(\int\frac{5x^4dx}{x^5(x^5+3)}\)

Put x⁵ = z

⇒ 5x⁴ dx = dz