Question

$\int \frac{10x^9+{10}^x{\log }_{e^{10}}dx}{x^{10}+{10}^x}$ equals

Answer 1

Given:
$\int \frac{({10x}^9+{10}^x\ln 10)dx}{{(x}^{10}+{10}^x)}$
To evaluate
solution;
take $y=x^{10}+{10}^x\frac{dy}{dx}={10x}^9+{10}^x\ln 10dy={(10x}^9+{10}^x\ln 10)dx\therefore I=\int \frac{dy}{y}=\ln y$
hence the correct answer is $\ln \left|(x^{10}+{10}^x)\right|$