How do you find the antiderivative of #2/(xsqrtx)#?

Answer 1

Rewrite it as #2x^(-3/2)# then apply the power rule for antiderivatives.

Add #1# to the exponent and divide by the new exponent.
#2x^(-3/2+1)/(-3/2+1) = 2x^(-1/2)/(-1/2) = -4x^(-1/2)+C#

Examine your response by making a distinction.

Try writing the solution without using any negative exponents.

#(-4)/x^(1/2) +C#

In the absence of logical exponents:

#(-4)/sqrtx +C#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the antiderivative of ( \frac{2}{x\sqrt{x}} ), you can use the substitution method. Let ( u = \sqrt{x} ), then ( x = u^2 ) and ( dx = 2u du ). Substitute these into the integral:

[ \int \frac{2}{x\sqrt{x}} , dx = \int \frac{2}{u^2 u} \cdot 2u , du ]

Simplify:

[ \int \frac{4}{u^3} , du ]

Now integrate with respect to ( u ):

[ \int \frac{4}{u^3} , du = 4 \int u^{-3} , du = 4 \left( \frac{u^{-2}}{-2} \right) + C ]

Substitute back ( u = \sqrt{x} ):

[ = -\frac{2}{\sqrt{x}^2} + C = -\frac{2}{x} + C ]

So, the antiderivative of ( \frac{2}{x\sqrt{x}} ) is ( -\frac{2}{x} + C ), where ( C ) is the constant of integration.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7