integration of x2+1

The integral


can be found by using the first Euler’s substitution (


but another possibility is to use partial integration ( if one knows the integral ∫d⁒xx2+1.  The corresponding may be said of the more general


We think that the integrand of I has the other factor 1 and integrate partially:


Writing the numerator as (x2+1)-1 and dividing its minuend and subtrahend separately, we can write


Having I in two , we solve it from these equalities, obtaining



Title integration of x2+1
Canonical name IntegrationOfsqrtx21
Date of creation 2013-03-22 18:06:58
Last modified on 2013-03-22 18:06:58
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Derivation
Classification msc 26A36
Synonym antiderivative of x2+1
Related topic IntegrationByParts
Related topic AreaFunctions
Related topic DerivativeOfInverseFunction