Mathematics

# $\displaystyle \int\frac{10x^{9}+10^{x}\log _{e}10}{10^{x}+x^{10}}dx.$

$\displaystyle \log \left ( 10^{x}+x^{10} \right ).$

##### SOLUTION
Let $\displaystyle I=\int \frac { 10x^{ 9 }+10^{ x }\log _{ e } 10 }{ 10^{ x }+x^{ 10 } } dx$
Put $\displaystyle 10^{ x }+x^{ 10 }=t\Rightarrow \left( 10x^{ 9 }+10^{ x }\log _{ e } 10 \right) dx=dt$
Therefore
$\displaystyle I=\int { \frac { dt }{ t } } =\log { t } =\log { \left( 10^{ x }+x^{ 10 } \right) }$
Hence, option 'C' is correct.

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

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