Complete Question
The complete question is shown on the first uploaded image
Answer:
The integral is divergent
Explanation:
From the question we are told that
The equation given is

Let

=>

=>

So

=>
![\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = 35 [(u^2)/(2) ] | \left {\infty } } \atop {1}} \right.](https://img.qammunity.org/2021/formulas/mathematics/college/4442c6tzyyb7x479p9vhrn9ualx91bjhcq.png)
=>
![\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [(ln (x))^2] | \left {\infty } } \atop {1}} \right.](https://img.qammunity.org/2021/formulas/mathematics/college/js5n5j89ovmmp07p58uq9i5t5wamv28e66.png)
=>
![\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [ [(ln (\infty))^2] - [(ln (1))^2] ]](https://img.qammunity.org/2021/formulas/mathematics/college/201ictuwunvtf3klw997da2vpmmo21blk0.png)
=>
![\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [ \infty - [(ln (1))^2] ]](https://img.qammunity.org/2021/formulas/mathematics/college/qdwr9jx435mgzlki4p862pj4mobij1yncu.png)
=>
![\int\limits^(\infty)_1 {35 (ln(x))/(x) } \, dx = (35)/(2) [ \infty ]](https://img.qammunity.org/2021/formulas/mathematics/college/5psxl515434jerk4hz7qi4x3stgpi0qpzs.png)
=>

Hence given that the solution to the integral is
then it mean that the integral is divergent