Category: Integration

Question Number 20385 by tammi last updated on 26/Aug/17 $$\int \sqrt{16-9x^{2}dx}$$ Answered by ajfour last updated on 26/Aug/17 $$=3\int \sqrt{{\left(\frac{4}{3}\right)}^2-x^2}dx$$$$=\frac{\mathrm{3}{x}}{\mathrm{2}}\sqrt{\left(\frac{\mathrm{4}}{\mathrm{3}}\right)^{\mathrm{2}}…

Question Number 20383 by tammi last updated on 26/Aug/17 $$\int \frac{dx}{x\sqrt{2+{\left(x\right)}^{\frac{1}{3}}}}$$ Answered by $@ty@mlastupdatedon26/Aug/17$${let}\:\mathrm{2}+{x}^{\frac{\mathrm{1}}{\mathrm{3}}} ={t}^{\mathrm{2}} \Rightarrow{x}=\left({t}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{3}} \…

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} \…