** Final Answer

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** Step-by-step Solution **

Problem to solve:

** Specify the solving method

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We can solve the integral $\int\sqrt{2w+1}dw$ 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 $2w+1$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

Learn how to solve integral calculus problems step by step online.

$u=2w+1$

Learn how to solve integral calculus problems step by step online. Integrate int((2w+1)^1/2)dw. We can solve the integral \int\sqrt{2w+1}dw 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 2w+1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dw in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dw in the previous equation. Substituting u and dw in the integral and simplify.

** Final Answer

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