Final answer to the problem
$\ln\left|x-2\right|+\frac{1}{\sqrt{3}}\arctan\left(\frac{x+1}{\sqrt{3}}\right)+4\ln\left|\sqrt{\left(x+1\right)^2+3}\right|+C_1$
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Step-by-step Solution
How should I solve this problem?
- Integrate using trigonometric identities
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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1
Find the integral
$\int\left(\frac{3}{x-2}+\frac{2x+3}{x^2+2x+4}+\frac{-\left(6x+12\right)}{x^3-8}\right)dx$
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$\int\left(\frac{3}{x-2}+\frac{2x+3}{x^2+2x+4}+\frac{-\left(6x+12\right)}{x^3-8}\right)dx$
Learn how to solve problems step by step online. Integrate the function 3/(x-2)+(2x+3)/(x^2+2x+4)(-(6x+12))/(x^3-8). Find the integral. Simplify the expression. The integral \int\frac{3}{x-2}dx results in: 3\ln\left(x-2\right). The integral \int\frac{-6x-12}{x^3-8}dx results in: -\int\frac{6x+12}{x^3-8}dx.
Final answer to the problem
$\ln\left|x-2\right|+\frac{1}{\sqrt{3}}\arctan\left(\frac{x+1}{\sqrt{3}}\right)+4\ln\left|\sqrt{\left(x+1\right)^2+3}\right|+C_1$
