Question

The value of $\int e^x(x^5+5x^4+1).dx$ is

• A. $e^x.x^5+e^x+C$
• B. $e^x.x^5$
• C. $5x^4.e^x$
• D. $e^{x+1}.x^5+C$

Answer 1

Answer: (A)

Let $I=\int e^x\left(x^5+5x^4+1\right)dx$
$=\int e^x{x}^{5}dx+5\int e^x{x}^{4}dx+\int e^{x}dx$
$=x^5{e}^x-\int 5x^4{e}^{x}dx+5\int e^x{x}^{4}dx+e^x$
$=x^5{e}^x+e^x+c=e^x\left(x^5+1\right)+c$