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Category: Integration

x-1-x-1-3-dx-

Question Number 20540 by tammi last updated on 28/Aug/17 $$\int\frac{\sqrt{{x}}}{\mathrm{1}+{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }{dx} \\ $$ Answered by $@ty@m last updated on 31/Aug/17 $${Let}\:{x}={t}^{\mathrm{6}} \:\:\:\:\left({Remark}:\:{LCM}\:{of}\:\mathrm{3}\:\&\:\mathrm{2}=\mathrm{6}\right) \\ $$$$\Rightarrow{dx}=\mathrm{6}{t}^{\mathrm{5}} {dt}…

xdx-x-1-x-2-1-

Question Number 20541 by tammi last updated on 28/Aug/17 $$\int\frac{{xdx}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$ Answered by $@ty@m last updated on 29/Aug/17 $${Let}\:\frac{{x}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)}=\frac{{A}}{{x}−\mathrm{1}}+\frac{{Bx}+{C}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\Rightarrow{A}\left({x}^{\mathrm{2}}…

2x-5-x-3-1-x-3-4x-dx-

Question Number 86039 by ar247 last updated on 26/Mar/20 $$\int\frac{\mathrm{2}{x}^{\mathrm{5}} −{x}^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{4}{x}}{dx} \\ $$ Commented by abdomathmax last updated on 27/Mar/20 $${A}\:=\int\:\:\frac{\mathrm{2}{x}^{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{4}{x}\right)+\mathrm{7}{x}^{\mathrm{3}}…

dx-2-4-

Question Number 86034 by ar247 last updated on 26/Mar/20 $$\int\frac{{dx}}{\:\sqrt{×^{\mathrm{2}} +\mathrm{4}}} \\ $$ Answered by TANMAY PANACEA. last updated on 26/Mar/20 $${x}=\mathrm{2}{tana}\:\:\frac{{dx}}{{da}}=\mathrm{2}{sec}^{\mathrm{2}} {a} \\ $$$$\int\frac{\mathrm{2}{sec}^{\mathrm{2}}…