Struggling with an Integral? Try These Substitution Strategies!

[adelin]

I cannot find a substitution that work for this integral

∫dx/2√x+2x

what should I do?

 

[statdad]

What is $\left(\sqrt{x}\right)^2$?

 

[adelin]

it is∫dx/2sqrt(x)+2x

 

[PhysicoRaj]

See what you can do to bring a function and it's derivative.. you have √x in the denominator so you should think in terms of derivative of that.

 

[statdad]

If the integral is
$$\int \frac{1}{2 \sqrt{x} + 2x} \, dx$$

thinking about the derivative of $\sqrt{x}$ alone will not help.

 

[adelin]

yes, this is the integral

 

[PhysicoRaj]

If he tries to bring the derivative of √x so that it is in product with the original function √x, he can substitute easily. That's what I meant.

 

[PhysicoRaj]

Convert the addition form in the denominator into product form so that the function and it's derivative are seen clearly in multiplied form.

 

[vanhees71]

Then think about the obvious substitution, aiming to get rid of the square root :-).

 

[adelin]

thank you