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Category: Integration

4-8-x-x-dx-

Question Number 86138 by jagoll last updated on 27/Mar/20 $$\int\underset{−\mathrm{4}} {\overset{\mathrm{8}} {\:}}\:\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$ Commented by Prithwish Sen 1 last updated on 27/Mar/20 $$\mathrm{l}\underset{\epsilon\rightarrow\mathrm{0}} {\mathrm{t}}\:\left\{\int_{−\mathrm{4}}…

sin-x-cos-x-sin-2x-dx-

Question Number 86091 by jagoll last updated on 27/Mar/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx} \\ $$ Commented by john santu last updated on 27/Mar/20 $${in}\:{other}\:{way} \\ $$$$\int\:−\frac{{d}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)}{\:\sqrt{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} −\mathrm{1}}}\: \\…

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}}…