Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 36538 by tanmay.chaudhury50@gmail.com last updated on 03/Jun/18

$$\int \frac{dx}{(a+{bx}^2)\sqrt{b-{ax}^2}}$$

Commented by abdo.msup.com last updated on 03/Jun/18

$$wehaveb-{ax}^2=b(1-{\left(\sqrt{\frac{a}{b}}x\right)}^{2}if\frac{a}{b}>0$$$$changement\sqrt{\frac{a}{b}}x=sin\left(t\right)give$$$$\frac{a}{b}x={sin}^{2}t\Rightarrow x=\frac{b}{a}{sin}^{2}t\Rightarrow$$$$I=\int \frac{1}{(a+b\frac{b^2}{a^2}{sin}^{4}t)\sqrt{b.}\sqrt{\frac{a}{b}}cost}\frac{2b}{a}sintcostdt$$$$=\frac{2b}{a}\int \frac{sint}{\sqrt{a}(a^3+b^3{sin}^{4}t)}{a}^{2}dt$$$$=\frac{2b}{\sqrt{a}}\int \frac{sint}{a^3+b^3{sin}^{4}t}dt...becontinued...$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com