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Integrals — MATHS STD 12 Science — Question

Rajasthan 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 $x^{10} + 10^x = t$
$\Rightarrow (10x^9 + 10^x \log_e10)dx = dt$
$\Rightarrow \int \frac{10 x^{9}+10^{x} \log _{e} 10}{x^{10}+10^{x}} d x=\int \frac{d t}{t}$
$= \log t + C$
$= \log(x^{10} + 10^x) + C$

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