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Learn how to solve problems step by step online. Integrate the function (x(x+1))^1/2. Find the integral. Solve the product x\left(x+1\right). Rewrite the expression \sqrt{x^2+x} inside the integral in factored form. We can solve the integral \int\sqrt{\left(x+\frac{1}{2}\right)^2-\frac{1}{4}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+\frac{1}{2} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.
Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more