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** Step-by-step Solution **

Problem to solve:

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We can solve the integral $\int x^2\sqrt{3x^3+4}dx$ 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 $3x^3+4$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

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$u=3x^3+4$

Learn how to solve integral calculus problems step by step online. Integrate int(x^2(3x^3+4)^1/2)dx. We can solve the integral \int x^2\sqrt{3x^3+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 3x^3+4 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 dx 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 dx in the previous equation. Substituting u and dx in the integral and simplify.

** Final Answer

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