Fill in the blank :
If `n ne-1`, then `int{f(x)}^(n).f'(x)dx=____________ +c,c` is a constant.

Fill in the blank : If f(x)=e^(x),g(x)=2log_(e)x" and "F(x)=f{g(x)} , then (dF)/(dx) = _________ .

If int f(x) dx=f(x) , then int {f(x)}^(2)dx is equal to -

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

int 1/f(x) dx = Inabs(f(x))^2 + c then, f(x) is

If f(x)is integrable function in the interval [-a,a] then show that int_(-a)^(a)f(x)dx=int_(0)^(a)[f(x)+f(-x)]dx.

If int(e^x-1)/(e^x+1)dx= f(x) +c, then find f(x).

inte^x(1+x)sec^2(xe^x)dx= f(x) +constant, then find f(x)

Show that inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

If f(x) is continuous for all real values of x , then sum_(r=1)^nint_0^1f(r-1+x)dx is equal to (a) int_0^nf(x)dx (b) int_0^1f(x)dx (c) int_0^1f(x)dx (d) (n-1)int_0^1f(x)dx

int (f'(x))/(f(x))dx is equal to-