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- Integrate using basic integrals
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Product of Binomials with Common Term
- FOIL Method
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Expand the fraction $\frac{x+1}{x^2-25}$ into $2$ simpler fractions with common denominator $x^2-25$
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$\int_{0}^{2}\left(\frac{x}{x^2-25}+\frac{1}{x^2-25}\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (x+1)/(x^2-25) from 0 to 2. Expand the fraction \frac{x+1}{x^2-25} into 2 simpler fractions with common denominator x^2-25. Expand the integral \int_{0}^{2}\left(\frac{x}{x^2-25}+\frac{1}{x^2-25}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2}\frac{x}{x^2-25}dx results in: \lim_{c\to0}\left(\ln\left(\frac{\sqrt{-21}}{2}\right)-\ln\left(\frac{\sqrt{c^2-25}}{c}\right)\right)+\lim_{c\to0}\left(-\ln\left(\frac{5}{2}\right)+\ln\left(\frac{5}{c}\right)\right). Gather the results of all integrals.