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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
$\int \frac{10 x^{9}+10^{x} \log _{e} 10 d x}{x^{10}+10^{x}}$, equals
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Answer

Let $x^{10}+10^x=t$
$\Rightarrow\left(10 x^9+10^x \log _e 10\right) d x=d t$
$\Rightarrow \int \frac{10 x^{9}+10^{x} \log _{e} 10}{x^{10}+10^{x}} d x=\int \frac{d t}{t}$
$= \log t + C$
$= \log(x^{10} + 10^x) + C$

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