Evaluate ≤ft(x+1/x)²dx

Correct Answer is : x33+2x− 1x+c\;{x³}{3}+2x-\;1/x+c3x3+2x−x1+c

Correct Answer is : x33+2x− 1x+c\;{x³}{3}+2x-\;1/x+c3x3+2x−x1+c

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Integral Calculus

Question : 43 of 73

Marks: +1, -0

Evaluate

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

Solution:

Concept:

Expand the square and integrate term by term using standard power rule.

Explanation:

Expand:

(x + \frac{1}{x})^2 = x^2 + 2 + \frac{1}{x^2}

Integrate each term:

\int x^2 dx = \frac{x^3}{3}

\int 2 dx = 2x

\int \frac{1}{x^2} dx = \int x^{-2} dx = -x^{-1} = -\frac{1}{x}

Combine with constant of integration:

\frac{x^3}{3} + 2x - \frac{1}{x} + C

Answer:

\frac{x^3}{3} + 2x - \frac{1}{x} + C

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