Can someone solve this Integral for me,please?

[Elena Baby]

Hello,I'm just learning Integral.So this is the question:

Thanks.~

 

[Deleted member 4993]

Hello,I'm just learning Integral.So this is the question:
View attachment 15392
Thanks.~

Have you learned "integration by parts" - which states:

\(\displaystyle \int u(x) dv \ = \ u(x) \cdot v(x) - \int v(x) du\)

 

[pka]

Hello,I'm just learning Integral.So this is the question: View attachment 15392

HINT: If \(\displaystyle y=x\cdot\log(x)-x\) then \(\displaystyle \frac{dy}{dx}=~?\)____________ [Here \(\displaystyle \log(x)\text{ is }\ln(x).\)]

 

[hoosie]

 

[Elena Baby]

Thanks everyone for helping!