Question

${\int }_1^t\frac{e^x}{x}(1+xlogx)dx=$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

${\int }_1^t\frac{e^x}{x}(1+xlogx)dx={\int }_1^t\frac{1}{x}{e}^{x}dx+{\int }_1^x{e}^{x}lo{g}_{e}xdx$
$={\left[e^{x}logx\right]}_1^4-{\int }_1^t{e}^{x}logxdx+{\int }_1^t{e}^{x}logxdx$
$=[e^{t}loge-e^{1}lo{g}_{4}1]=e^t$