Integral Solution for 2/√x3 + 3√x | Homework Help

[lubo]

Homework Statement

∫ (2/√x³ + 3√x) dx

Homework Equations

Xⁿdx = xⁿ⁺¹/n+1 +C

The Attempt at a Solution

∫(2/(x³)^^1/2 + 3x^1/2) dx

∫(2/x^3/2+ 3x^1/2) dx

∫(2x^-3/2+ 3x^1/2) dx

= 2x^-1/2/-1/2 + 3x^3/2/(3/2) +C

= -4x^-1/2 + 2x^3/2 +C

= -4/x^1/2 + 2x^3/2 +C

Can you please confirm the above answer as I have no answers to compare and am not 100% sure on this one?

Thank you for any help in advance

 

[Simon Bridge]

Try the Wolfram integrator.

What you really really need is some way of being able to check your integrals without having to refer to some authority like this. You start by seeing if you can describe what it is about the answer that makes you unsure of it. Is it something to do with the conversion of surds to fractional powers? The use of negative powers? Or just the rule for integrating a power?

Having identified the problem, you can work out how to test it.

 

[lubo]

Thanks. The program above worked. I have a new calculator and it is showing me the wrong result and with no answer? This program solved it easy.

 

[jedishrfu]

You really didn't need a calculator to check your answer.

You can check your answer by differentiating it to see if you get back the original. In your case, it works.

Trust in the force, Luke.

 

[lubo]

Jedishrfu - Now that is cool also, I did forget about this as it is a long time since I was taught it. Thanks.