Manually written function doesn't behave the same as the gamma function - r

Question

So I implemented a function that calculates the value of the gamma function. and when I try to multiply f5(a) with a numeric I receive the error : Error in result * f5(a) : non-numeric argument to binary operator and if I instead use result * gamma(a) which is the predefined function it works just fine. It seems like it won't let me do any arithmetic operation with f5 even though it returns the same result as gamma
f5 <- function(a)
{
f <- function(x)
x^(a-1)*exp(-x)
integrate(f, 0, Inf)
}
f6 <- function(a)
{
if (a < 0)
print("a is negative")
else if (a%%1 == 0)
return (factorial(a-1))
else
{
result <- 1
while (a > 1)
{
result <- result * (a - 1)
a <- a - 1
}
result <- result * f5(a)
result
}
}
gamma(0.3)
f5(0.3)
f6(0.3)

Answer 1

This is because of the class of object that gets returned from f5().
class(f5(0.3))
[1] "integrate"
This is a named list object, and you can call the specific value from it:
names(f5(a))
[1] "value" "abs.error" "subdivisions" "message" "call"
You want the value component. Modifying f6() to the code below makes it work:
f6 <- function(a){
if (a < 0){
print("a is negative")
}else if (a%%1 == 0){
return (factorial(a-1))
}else{
result <- 1
while (a > 1){
result <- result * (a - 1)
a <- a - 1
}
result <- result * f5(a)$value
result
}
}