Step-by-step Solution

Integrate $\frac{1}{\left(x+1\right)^2}$ from $0$ to $\infty $

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Step-by-step explanation

Problem to solve:

$\int_0^{\infty}\left(\frac{1}{\left(x+1\right)^2}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\lim_{c\to\infty }\:\int_{0}^{c}\frac{1}{\left(x+1\right)^2}dx$

Unlock this full step-by-step solution!

Learn how to solve definite integrals problems step by step online. Integrate 1/((x+1)^2) from 0 to \infty. Replace the integral's limit by a finite value. Apply the formula: \int\frac{n}{\left(x+a\right)^c}dx=\frac{-n}{\left(c-1\right)\left(x+a\right)^{\left(c-1\right)}}, where a=1, c=2 and n=1. Evaluate the definite integral. The limit of a sum of two functions is equal to the sum of the limits of each function: \displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x)).

Final Answer

$1$

Problem Analysis