Question
Integrate the following functions w.r.t. x:
$\frac{10^9+10^2 \cdot \log 10}{10^2+x^{10}}$
✓
Answer
Let $I=\int \frac{10 x^9+10^x \cdot \log 10}{10^x+x^{10}} d x$
Put $10^x+x^{10}=t$
$\therefore\left(10^x \cdot \log 10+10 x^9\right) d x=d t$
$\therefore I=\int \frac{1}{t} d t=\log |t|+c$
$=\log \left|10^x+x^{10}\right|+c$
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