Question

Evaluate: $\int {(x}^4+6x+2)dx$

• A. $\frac{x^5}{5}+6\frac{x^2}{2}+2x$
• B. $\frac{x^5}{5}+6\frac{x^2}{2}+2x+C$
• C. $\frac{x^6}{5}+6\frac{x^2}{2}+2x+C$
• D. All of the above

Answer 1

The correct option is B $\frac{x^5}{5}+6\frac{x^2}{2}+2x+C$

$I=\int (x^4+6x+2)dx=\int x^{4}dx+6\int xdx+2\int dxI=\frac{x^5}{5}+6\frac{x^2}{2}+2x+C\{\because \int x^{n}dx=\frac{x^{n+1}}{n+1}+C\}$