Integrating a Quadratic Divided by the Square Root of a Quadratic

This Demonstration shows the calculation of the indefinite integral . Such an integral is equal to . The coefficients , , and are found by differentiating the equality, getting rid of the denominator, and comparing the coefficients of equal powers of on the left and on the right.

The algebraic part can be separated from the integral by the formula

,

where . The coefficients are found by differentiating the equality and getting rid of the denominator by comparing the coefficients of equal powers of on the left and on the right.

Reference

[1] V. P. Minorsky, Problems in Higher Mathematics, Moscow: Mir Publishers, 1975 pp. 188–189.