Mathematics: HELP Please Simplifying Expressions by Combining Like Terms Combine the like terms in each expression to find the matching simplified expression. y +X-2 - 6x X 5xy + 4x - 5xy - 3x x-1 2x + 3-X-4 y -5x - 2

The solution is Step-by-step explanation:From the question The function given is The indefinite integral is mathematically represented as Now let = = So Now substituting for u...

HELP Please Simplifying Expressions by Combining

Ответ:

kkeith121p6ujlt

12.08.2021

Mathematics

The solution is $\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C$

Step-by-step explanation:

From the question

The function given is $f(x) = \frac{e^{2x}}{ 25 + e^{4x}} dx$

The indefinite integral is mathematically represented as

$\int\limits {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx$

Now let $e^{2x} = u$

=> $\frac{du}{dx} 2e^{2x}$

=> $2 e^{2x}dx = du$

$\int\limits {\frac{e^{2x}}{ 25 + e^{4x}}} \, dx = \int\limits {\frac{1}{ 2(25 + u^2)} } \, du$

$= \frac{1}{2} \int\limits {\frac{1}{ 25 + u^2)} } \, du$

$= \frac{1}{2} \int\limits {\frac{1}{ 5^2 + u^2)} } \, du$

$= \frac{1}{2} \frac{tan^{-1} [\frac{u}{5} ]}{5} + C$

Now substituting for u

$\frac{1}{10} * tan^{-1}[\frac{e^{2x}}{5} ] + C$

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HELP Please Simplifying Expressions by Combining Like Terms
Combine the like terms in each expression to find the matching simplified expression.
y +X-2 - 6x
X
5xy + 4x - 5xy - 3x
x-1
2x + 3-X-4
y -5x - 2

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