Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$

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

$\frac{1}{x\left(x+1\right)}=\frac{A}{x}+\frac{B}{x+1}$

Unlock this full step-by-step solution!

Learn how to solve definite integrals problems step by step online. Integrate 1/(x(x+1)) from 1 to 2. Rewrite the fraction \frac{1}{x\left(x+1\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by x\left(x+1\right). Multiplying polynomials. Simplifying.

Final Answer

$0.2877$