Integration of the form `(f'(x)) / f(x) dx`

Integration of form e^(x)(f(x)+f'(x))dx

Integral of form (f(x))^(n)f'(x)dx

Consider the integral I=int(xe^(x))/((1+x)^(2))dx Express the integral I in the form inte^(x)(f(x)+f'(x))dx

Integrate the functions f(x) f(x)=x log(x)

Read the following passages and answer the following questions (7-9) Consider the integrals of the form l=inte^(x)(f(x)+f'(x))dx By product rule considering e^(x)f(x) as first integral and e^(x)f'(x) as second one, we get l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c int((1)/(lnx)-(1)/((lnx)^(2)))dx is equal to

Read the following passages and answer the following questions (7-9) Consider the integrals of the form l=inte^(x)(f(x)+f'(x))dx By product rule considering e^(x)f(x) as first integral and e^(x)f'(x) as second one, we get l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c l=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx then l is equal to

Read the following passages and answer the following questions (7-9) Consider the integrals of the form l=inte^(x)(f(x)+f'(x))dx By product rule considering e^(x)f(x) as first integral and e^(x)f'(x) as second one, we get l=e^(x)f(x)-int(f(x)+f'(x))dx=e^(x)f(x)+c l=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx then l is equal to

Consider the integral I=int(xe^x)/(1+x)^2dx Express the integral I in the form of inte^x{f(x)+f'(x)}dx .