Daftar integral dari fungsi irasional: Perbedaan antara revisi

 

== Integral melibatkan <math>R = \sqrt{ax^2+bx+c}</math> ==

 

: <math>\int\frac{dx}{R} = \frac{1}{\sqrt{a}}\ln\left|2\sqrt{a}R+2ax+b\right| \qquad \mbox{(untuk }a>0\mbox{)}</math><!-- (4.1) [Abramowitz & Stegun p13 3.3.33] + verified by differentiation -->

: <math>\int x^n \sqrt{ax + b}\,dx \; = \; \frac{2}{2n +1}\left(x^{n+1} \sqrt{ax + b} + bx^{n} \sqrt{ax + b} - nb\int x^{n-1}\sqrt{ax + b}\,dx \right) </math>

 

* Milton Abramowitz and Irene A. Stegun, eds., ''[[Handbook of Mathematical Functions]] with Formulas, Graphs, and Mathematical Tables'' 1972, Dover: New York. ''(See [http://www.math.sfu.ca/~cbm/aands/page_13.htm chapter 3].)''