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Evaluate the given integral.$$\int\left(2 x^{2}-3 x y^{3}+y^{2}+3\right) d x$$

$$\frac{2 x^{3}}{3}-\frac{3 x^{2} y^{3}}{2}+x y^{2}+3 x+c(y)$$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 6

Double Integrals

Partial Derivatives

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Hello in this video. I'll show how to evaluate this integral here. So you've always appreciate it. Yeah. Then we also have a TX which represents with respect to X. So inside the this expression market function. Another you see that we have some constants. Who I'm pretty sure you know that to it as a constant. These numbers three years is a constant and plus this three as a concern. But also we have why? Why here? And how do we treat this wise? So what's important to look at is this D expert. This takes part means that we are integrating with respect to X. So everything inside this expression which is not an X. We treat it as a constant. Okay so he's wise. What do the part three is also concerned? Why do the part 2? It's also a constant. So answering this, you know our treasure our constants. So firstly we have two extra report to you know that this becomes two x. 2 or three home three. My ass. So the F. Our three X. Y. to the Power three. Especially you can write this three. Why two or 3 or consent. And then we have eggs. We know that it's going to become next to report to over to. And then we have Y. To the part to you know that Why do the country is a constant? So when they have waited for two x. Then last two years plus three which becomes plus three X. Then remember this is an indefinite integral. So you need to add plus C. So this becomes the integral of a function here. Thank you for.

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