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

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

Integral of the form: (ax+b)^(n)P(x)dx;P(x)/((ax+b)^(n))dx

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

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

The value of int[f(x)]^(n)f'(x)dx=

If intg(x)dx=g(x) , then the value of the integral intf(x)g(x){f(x)+2f'(x)}dx is

The value of integral int _(0)^(pi) x f (sin x ) dx is

Integration OF ( dx / a Sinx + b Cosx ) type || Integration OF [ e^x( f(x)+f'(x) ] type || Excercise 1 - Q 27, Ex - level 1 ( Q 7)