Evaluate: `inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C`

If intg(x)dx=g(x) , then evaluate intg(x){f(x)+f^(prime)(x)}dx

Statement 1: int(xe^(x)dx)/((1+x)^(2))=(e^(x))/(x+1)+C Statement 2: inte^(x)(f(x)+f'(x))dx=e^(x)f(x)+C

int[f(a x+b)]^nf^(prime)(a x+b)dx

Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: inte^x x^x(2+logx)= (A) e^x x^xlogx+C (B) e^x+x^x+C (C) e^x x(logx)^2+C (D) e^x.x^x+C

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: int(e^x(2-x^2))/((1-x)sqrt(1-x^2))dx (A) e^xsqrt((1-x)/(1+x))+C (B) e^xsqrt((1+x)/(1-x))+C (C) e^xsqrt((2-x)/(2+x))+C (D) none of these

The integral inte^x(f(x)+f\'(x))dx can be solved by using integration by parts such that: I=inte^xf(x)dx+inte^xf\'(x)dx=e^xf(x)-inte^xf\'(x)dx+inte^xf\'(x)dx=e^xf(x)+C , and inte^(ax)(f(x)+(f\'(x))/a)dx=e^(ax)f(x)/a+C ,Now answer the question: int{log_e(log_ex)+1/(log_ex)^2}dx is equal to (A) log_e(log_ex)+C (B) xlog_e(log_ex)-x/log_ex+C (C) x/log_ex-log_ex+C (D) log_e(log_ex)-x/log_ex+C

Evaluate: int(x)i spol y nom i a lfu n c t ionoft h en t h degr e e ,p rov et h a t- inte^xf(x)dx=e^x[f(x)f^(prime)(x)+f^(x)=f^(x)++(-1)^nf^((n))(x)] Where f^((n))(x)d e not e s(d^nf)/(dx^n)

Write a value of inte^(a x)\ {a\ f\ (x)+f^(prime)(x)}\ dx

The integral I=inte^(x)((1+sinx)/(1+cosx))dx=e^(x)f(x)+C (where, C is the constant of integration). Then, the range of y=f(x) (for all x in the domain of f(x) ) is