Question

$4\int \frac{a^6+x^8}{x}dx$ is equal to

• A. $4a^6\log a+\frac{x^8}{8}+C$
• B. $a^6\log x+\frac{x^8}{8}+C$
• C. $4a^6\log x+\frac{x^8}{8}+C$
• D. $4a^6\log x+\frac{x^8}{2}+C$

Answer 1

The correct option is D $4a^6\log x+\frac{x^8}{2}+C$

Let $I=4\int \frac{a^6+x^8}{x}dx$
$I=4\int \frac{a^6}{x}dx+\frac{x^8}{x}dx$
$I=4a^6\log x+4.\frac{x^8}{8}+C$