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Category: Integration

Express-1-5-9-in-partial-fraction-

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

1-7-1-1-7-e-x-dx-

Question Number 85875 by sakeefhasan05@gmail.com last updated on 25/Mar/20 $$\int\left(\frac{\mathrm{1}}{\mathrm{7}\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{7}}\mathrm{e}^{\mathrm{x}} \right]}\right)\:\mathrm{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 25/Mar/20 $$\frac{\mathrm{1}}{\mathrm{7}}\int\frac{{e}^{−{x}} {dx}}{{e}^{−{x}} −\frac{\mathrm{1}}{\mathrm{7}}}\:\left(\boldsymbol{{multiply}}\:\boldsymbol{{N}}_{{r}} {and}\:{D}_{{r}}…

x-1-x-2-1-dx-

Question Number 85839 by sahnaz last updated on 25/Mar/20 $$\int\mathrm{x}×\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\mathrm{dx} \\ $$ Commented by jagoll last updated on 25/Mar/20 $$\int\:\frac{\mathrm{x}\:\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} }…

a-x-x-dx-

Question Number 20293 by tammi last updated on 25/Aug/17 $$\int\sqrt{\frac{{a}+{x}}{{x}}{dx}} \\ $$ Answered by $@ty@m last updated on 25/Aug/17 $$=\int\frac{{a}+{x}}{\:\sqrt{{x}\left({a}+{x}\right)}}{dx} \\ $$$$=\int\frac{{a}+{x}}{\:\sqrt{{ax}+{x}^{\mathrm{2}} }}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}+{a}+{a}}{\:\sqrt{{ax}+{x}^{\mathrm{2}}…