Question

Don’t spam...

Otherwise your answers and ID both will be reported to a moderator. ​​

❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ

❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​​​​

Answer 1

$\displaystyle \sf \red{ \int \frac{ {x}^{ \frac{x}{ lnx } } }{ \sqrt{e} } \: dx }$

$\displaystyle \sf \red{ = \int \frac{ {e}^{ \cancel{lnx}} \cdot \frac{x}{2 \: \cancel{lnx } } }{ {e}^{ \frac{x}{2} } } \: dx }$

$\displaystyle \sf \red{ = \int \frac{{ \cancel{e}^{ \cancel{\frac{x}{2}}}}}{ { \cancel{e}^{ \cancel{\frac{x}{2}}} } } \: dx }$

$\displaystyle \sf \red{=\int 1 \:dx}$

$\displaystyle \sf \red{ = X+C}$

Answer 2

Step-by-step explanation:

We have,

$\displaystyle \tt \int \dfrac{x^{ \frac{x}{ \ln(x)} } }{ \sqrt{e} } \: dx$

$\displaystyle = \frac{1}{ \sqrt{e} } \tt \int \: x^{ \displaystyle \tt x \: log_{x}(e) } \: dx$

$\displaystyle = \frac{1}{ \sqrt{e} } \tt \int \: x^{ \displaystyle \tt \: log_{x}(e ^{x} ) } \: dx$

$\displaystyle = \frac{1}{ \sqrt{e} } \tt \int \: e ^{x} \: dx$

$\displaystyle = \dfrac{e^{x} }{ \sqrt{e} } + c$