(x + 1/x)^2 dx equals : Option 1: x^3/3 + 1/x - 2x + c Option 2: x^3/3 - 1/x + 2x + c Option 3: x^3/3 - 1/x - 2x + c Option 4: x^3/3 + 1/x + 2x + c

Answer: x^3/3 - 1/x + 2x + c. Solution: Expand: (x + 1/x)^2 = x^2 + 2 + 1/x^2. Integrating term by term gives x^3/3 + 2x - 1/x + c.

Calculus

Integrals

Easy

common

$\int \left(x + \frac{1}{x}\right)^2 dx$ equals :

$\frac{x^3}{3} + \frac{1}{x} - 2x + c$

$\frac{x^3}{3} - \frac{1}{x} + 2x + c$

$\frac{x^3}{3} - \frac{1}{x} - 2x + c$

$\frac{x^3}{3} + \frac{1}{x} + 2x + c$

✅ Correct Option: 2

Expand: $\left(x + \frac{1}{x}\right)^2 = x^2 + 2 + \frac{1}{x^2}$ . Integrating term by term gives $\frac{x^3}{3} + 2x - \frac{1}{x} + c$ .

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