Calculus Please Help?

Question

What is antiderivative of 1/sqrt5. I know it has to be with ln, but can't get the right answer?

Answer 1

Are you missing a variable in there? Because 1/sqrt 5 is a constant, and the antiderivative of a constant is just the product of that constant and the variable of antidifferentiation. So the antiderivative of 1/sqrt 5 dx would just be x/sqrt 5 + c.
Now if you mean 1/((sqrt 5) x) that would involve ln as you can see if you rewrote it as 1/(x (sqrt 5))
If you mean 1/(sqrt (5x)) that would not involve ln, that would integrate by the usual power rule.

Answer 2

If you haven't made a typo then that's the integral of a constant:

int/(1/sqrt(5))=1/sqrt(5)x

If it's:

int(1/sqrt(5x))

Let's rewrite it in a more familiar form:

int( (5x)^(-1/2) )

By the properties of exponents we can write the square root as root 1/2 and one over that gives us the minus sign. The anti derivative of a power rule is

int( x^n ) = 1/(n+1)x^(n+1)

Now apply the above rule to the integral to get the answer. Just be careful with the constant coefficient in front.

By the way, you get natural logs (ln) from integrals of the form:

int( 1/x )

Answer 3

1/sqrt5 x + C

There is no variable. This is a constant.

Answer 4

=x/√5 +c
cuz this is only a constant
if you had something like:
1/x√5
then the integral wud b
=(lnx)/√5 +c
we get ln only when the denominator has 'x^1'

Answer 5

For antiderivative, there must be variable. I think you question is wrong, because you give only constant not variable.

Answer 6

integral (x^-.5)dx

=(x^-1.5)/(-.5)