Evaluate the integral

[CatchThis2]

(1/x+2/sqrtx)dx

These are the values I used:

U=1/x
DU=lnx
dv=x^-1/2
v=2x^-1/2

Not sure if this is right or not or how to finish off the problem

 

[Deleted member 4993]

(1/x+2/sqrtx)dx

These are the values I used:

U=1/x
DU=lnx
dv=x^-1/2
v=2x^-1/2

Not sure if this is right or not or how to finish off the problem

Does your problem look like:

$\displaystyle \int \left (\frac{1}{x} + \frac{2}{\sqrt{x}} \right ) dx$

If yes then - that reduces to:

$\displaystyle = \int \frac{1}{x} dx + \int \frac{2}{\sqrt{x}} dx$

Those are elementary antiderivatives now....

 

[CatchThis2]

Yes it reduces to what you have which I did. How do you proceed from there?

 

[mmm4444bot]

Proceed by finding the antiderivatives.

Does it help to see the integrands written exponentially versus rationally/radically?

$\displaystyle = \int x^{-1} \ dx \;+\; \int 2x^{-1/2} \ dx$

 

[CatchThis2]

Yes, how do I solve from here? Do I uses U substitution?

 

[Deleted member 4993]

Yes, how do I solve from here? Do I uses U substitution?... No - not for most direct approach

Use

for n <> -1

$\displaystyle \int x^n dx = \frac{x^{n+1}}{n+1} + C$

for n = -1 you would have a standard anti-derivative.

 

[BigGlenntheHeavy]

$\displaystyle \int x^{-1} dx$

Yes it reduces to what you have which I did. How do you proceed from there?

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