Make substitution, then evaluate integral 1/[x*sqrt(x + 1)dx

[MarkSA]

Hello,

1) Make a substitution to express the integrand as a rational function and then evaluate the integral.

Integral of: 1/[x*sqrt(x + 1)] dx

Kind of confused, isn't it already a rational function? How would I do a substitution to make it one?

Thanks

 

[stapel]

Kind of confused, isn't it already a rational function?

Do you have polynomials for the numerator and denominator, or does the denominator contain a radical factor?

Hint: Try \(\displaystyle u\, =\, \sqrt{x\, +\, 1}\) :wink:

Eliz.

 

[Deleted member 4993]

In mathematics, a rational function is any function whose output can be given by a formula that is the ratio of two polynomials.

\(\displaystyle \sqrt\) is not included in "polynomials".