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

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

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

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

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

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

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)

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to a) -cosx (b) -sinx c) int_0^x(x-t)f(t)dt (d) 0

If f(x)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

Evaluate: (i) int(2^x+3^x)/(5^x)\ dx (ii) int((a^x+b^x)^2)/(a^x\ b\ ^x)\ dx

int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)} \ dx