Mathematics

# Evaluate the following integral$\int { \cfrac { 10{ x }^{ 9 }+{ 10 }^{ x }\log _{ e }{ 10 } }{ { 10 }^{ x }+{ x }^{ 10 } } } dx\quad$

##### SOLUTION
Let
$t={10}^{x}+{x}^{10}$

$\Rightarrow\,dt=\left({10}^{x}\log{10}+10{x}^{9}\right)dx$

$\displaystyle\int{\dfrac{10{x}^{9}+{10}^{x}\log{10}}{{10}^{x}+{x}^{10}}dx}$

$=\displaystyle\int{\dfrac{dt}{t}}$

$=\log{\left|t\right|}+c$

$=\log{\left|{10}^{x}+{x}^{10}\right|}+c$ where $t={10}^{x}+{x}^{10}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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