Integrating a Quadratic Divided by the Square Root of a Quadratic

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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.

Contributed by: Izidor Hafner (April 2014)
Open content licensed under CC BY-NC-SA


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Details

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.



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