Category: Integration

Question Number 85909 by jagoll last updated on 26/Mar/20 $$\int {\sin }^{-1}\left(\sqrt{\frac{\mathrm{x}}{\mathrm{a}+\mathrm{x}}}\right)\mathrm{dx},\mathrm{a}>0$$ Commented by john santu last updated on 26/Mar/20 $${let}\:\sqrt{\frac{{x}}{{a}+{x}}}\:=\:{n}\:\Rightarrow\:{x}\:=\:\frac{{an}^{\mathrm{2}} }{\mathrm{1}−{n}^{\mathrm{2}} } \…

Question Number 85896 by ar247 last updated on 25/Mar/20 Commented by abdomathmax last updated on 25/Mar/20 $$I=\int \frac{5x-5}{3x^2-8x-3}dx$$$$3x^2-8x-3=0\to {\mathrm{\Delta }}^{{}^{\prime }}=4^2-\left(3\right)(-3)=16+9=25$$$${x}_{\mathrm{1}}…

Question Number 151428 by peter frank last updated on 21/Aug/21 $$\int \frac{\mathrm{x}+2}{({\mathrm{x}}^2+3\mathrm{x}+3)\sqrt{\mathrm{x}+1}}\mathrm{dx}$$$$$$ Answered by MJS_new last updated on 21/Aug/21 $$\left(\mathrm{1}\right)\:\mathrm{trying}\:\mathrm{something} \…

Question Number 85890 by frc2crc last updated on 25/Mar/20 $$Isthereasumfor\psi \left(\frac{p}{q}\right)oranintegral$$$$foranyfractionp/q$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 151426 by peter frank last updated on 21/Aug/21 $$\mathrm{Express}\frac{1}{5\times 9}\mathrm{in}\mathrm{partial}\mathrm{fraction}$$ Answered by liberty last updated on 21/Aug/21 $$\frac{1}{\mathrm{n}(\mathrm{n}+4)}=\frac{\mathrm{a}}{\mathrm{n}}+\frac{\mathrm{b}}{\mathrm{n}+4}$$$$\mathrm{a}=\:\left[\frac{\mathrm{1}}{\mathrm{n}+\mathrm{4}}\:\right]_{\mathrm{n}=\mathrm{0}} =\frac{\mathrm{1}}{\mathrm{4}} \…