Question

$\int \frac{10x^9+10^x \log_e 10}{x^{10}+10^x}dx$ equals

• A. 10x - x10+C
• B. 10x+x10+C
• C. (10x+x10)-1 +C
• D. log(10x+x10)+C

Answer 1

Answer: (D)

log(10x+x10)+C

Answer 2

Let x10+10x = t

∴ (10x9+10x loge 10) dx=dt

$\Rightarrow \int \frac{10x^9+10^x \log_e 10}{x^{10}+10^x}dx=\int\frac{dt}{t}$

=log t+C

=log(10x+x10)+C

Hence, the correct Answer is D.