Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Find the integral
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$\int\left(\left(x+\frac{1}{x}\right)^2-\left(x+\frac{-1}{x}\right)^2\right)dx$
Learn how to solve integral calculus problems step by step online. Integrate the function (x+1/x)^2-(x+-1/x)^2. Find the integral. Expand the integral \int\left(\left(x+\frac{1}{x}\right)^2-\left(x+\frac{-1}{x}\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\left(x+\frac{1}{x}\right)^2dx results in: \frac{x^{4}+6x^2-3}{3x}. The integral \int-\left(x+\frac{-1}{x}\right)^2dx results in: \frac{-x^{4}+6x^2+3}{3x}.