use the table of integrals to evaluate the following integral.

$\int 3x\sqrt{6x-{x}^{2}}dx$

allhvasstH
2021-05-26
Answered

use the table of integrals to evaluate the following integral.

$\int 3x\sqrt{6x-{x}^{2}}dx$

You can still ask an expert for help

Viktor Wiley

Answered 2021-05-27
Author has **84** answers

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Evaluate the following integrals. Include absolute values.

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How do you find the primitive/integral of $\mathrm{arctan}x$ ?

I tried searching for how you derive the integral/primitive of$\mathrm{arctan}\left(x\right)$ , but I can't find any question on S.E with an answer that clearly explains this. I feel that there should be one, since it is rather fundamental knowledge, and it does come up every now and then as part of S.E questions.

So the primitive can be looked up and it should be the following:

$\int \mathrm{arctan}\left(x\right)dx=x\mathrm{arctan}\left(x\right)-\frac{1}{2}\mathrm{ln}(1+{x}^{2})+C$

How do you get the result?

I tried searching for how you derive the integral/primitive of

So the primitive can be looked up and it should be the following:

How do you get the result?

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Evaluate $\int \frac{4}{9}\ufeff{e}^{6x}\mathrm{tan}({e}^{6x}+4)\mathrm{sec}({e}^{6x}+4)dx$.

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Evaluate the integral.

$\int \frac{{(1+{e}^{x})}^{2}}{{e}^{x}}dx$