Final answer to the problem
The integral diverges.
Step-by-step Solution
How should I solve this problem?
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- 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
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1
Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number
$\int\frac{\frac{1}{x}+\frac{1}{x^{2}}}{1+x^2}dx$
Learn how to solve problems step by step online. Integrate the function (x^(-1)+x^(-2))/(1+x^2) from 0 to infinity. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Simplify the expression. Rewrite the fraction \frac{1+x}{x^{2}\left(1+x^2\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x^{2}}+\frac{-x-1}{1+x^2}+\frac{1}{x}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
The integral diverges.
